Data processing device and data processing method

ABSTRACT

The present technology relates to a data processing device and a data processing method capable of securing excellent communication quality in data transmission using an LDPC code. In group-wise interleave, an LDPC code having a code length N of 64800 bits and a coding rate r of 9/15, 11/15, or 13/15 is interleaved in units of bit groups of 360 bits. In group-wise deinterleave, a sequence of LDPC codes after the group-wise interleave is returned to an original sequence. The present technology, for example, can be applied to a case where data transmission using an LDPC code or the like is performed.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No. 15/980,374, filed on May 15, 2018, which is a continuation of U.S. application Ser. No. 15/122,439, filed Aug. 30, 2016, which is a National Stage of PCT/JP2015/056597, filed Mar. 6, 2015 and claims the benefit of priority under 35 U.S.C. § 119 of Japanese Patent Application No. 2014-056461, filed Mar. 19, 2014. The entire contents of each of the above-noted applications are incorporated herein by reference.

TECHNICAL FIELD

The present technology relates to a data processing device and a data processing method, and more particularly, to a data processing device and a data processing method capable of securing excellent communication quality, for example, in data transmission using an LDPC code.

BACKGROUND ART

Some of information presented in the present specification and drawings was provided by Samsung Electronics Co., Ltd. (hereinafter, represented as Samsung), LGE Inc., NERC, and CRC/ETRI (indicated in the drawings).

A low density parity check (LDPC) code has a high error correction capability, and in recent years, the LDPC code has widely been employed in transmission schemes of digital broadcasting such as Digital Video Broadcasting (DVB)-S.2, DVB-T.2, and DVB-C.2 of Europe and the like, or Advanced Television Systems Committee (ATSC) 3.0 of the USA and the like (for example, see Non-Patent Document 1).

From a recent study, it is known that performance near a Shannon limit is acquired from the LDPC code when a code length increases, similarly to a turbo code or the like. Since the LDPC code has a property that a shortest distance is proportional to the code length, the LDPC code has advantages of a block error probability characteristic being superior and a so-called error floor phenomenon observed in a decoding characteristic of the turbo code or the like rarely occurring as characteristics thereof.

CITATION LIST Non-Patent Document

-   Non-Patent Document 1: DVB-S.2: ETSI EN 302307 V1.2.1 (2009 October)

SUMMARY OF THE INVENTION Problems to be Solved by the Invention

In data transmission using the LDPC code, for example, the LDPC code is converted into a symbol of a quadrature modulation (digital modulation) such as Quadrature Phase Shift Keying (QPSK), and the symbol is mapped to a signal point of the quadrature modulation and is transmitted.

The data transmission using the LDPC code as above has spread worldwide, and there is a demand to secure excellent communication (transmission) quality.

The present technology is in consideration of such a situation and enables the securement of excellent communication quality in data transmission using an LDPC code.

Solutions to Problems

According to the present technology, there is provided a first data processing device/method including: a coding unit/step that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 9/15; a group-wise interleaving unit/step that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit/step that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

18, 8, 166, 117, 4, 111, 142, 148, 176, 91, 120, 144, 99, 124, 20, 25, 31, 78, 36, 72, 2, 98, 93, 74, 174, 52, 152, 62, 88, 75, 23, 97, 147, 15, 71, 1, 127, 138, 81, 83, 68, 94, 112, 119, 121, 89, 163, 85, 86, 28, 17, 64, 14, 44, 158, 159, 150, 32, 128, 70, 90, 29, 30, 63, 100, 65, 129, 140, 177, 46, 84, 92, 10, 33, 58, 7, 96, 151, 171, 40, 76, 6, 3, 37, 104, 57, 135, 103, 141, 107, 116, 160, 41, 153, 175, 55, 130, 118, 131, 42, 27, 133, 95, 179, 34, 21, 87, 106, 105, 108, 79, 134, 113, 26, 164, 114, 73, 102, 77, 22, 110, 161, 43, 122, 123, 82, 5, 48, 139, 60, 49, 154, 115, 146, 67, 69, 137, 109, 143, 24, 101, 45, 16, 12, 19, 178, 80, 51, 47, 149, 50, 172, 170, 169, 61, 9, 39, 136, 59, 38, 54, 156, 126, 125, 145, 0, 13, 155, 132, 162, 11, 157, 66, 165, 173, 56, 168, 167, 53, and 35,

the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

11315573316568062411040713404139471404014353 155221569816079173631937419543205302283324339

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485841012993786106681852318963208642210622308 2303323107231282399024286244092459525802

1251389465398276108851164412777134271403915954 1707819053205372286324521250872546325838

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59135051694123793

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8421130761427115401

9630141121901720955

212139322178125824

596191101665419636

585434993612770

65751143319798

2731733820926

142531846325404

217912480525869

21164615850

6075858623819

184352209324852

2103236811704

109251740218232

90622506125674

184972085323404

186061936419551

7102225543

67441548125868

90811730525164

82370125883

96801995522848

56456419121

55951508625892

31741712723183

193971981720275

125612457125825

7111988925865

191042018921851

549968625548

65862032525906

32242071021637

6411521525754

134842372925818

2043749324246

168602523025768

220472420024902

93911804019499

78552433625069

238342557025852

1977880025756

66712177225859

3279671024444

240992511725820

55531230625915

481110723907

108321197425773

22231790525484

167821713520446

47528613457

162182244924362

117162220025897

83151500922633

132048025852

123521865825687

36811479423703

302453125846

41032207724107

238372562225812

36271338725839

908536719388

0689425795

203222354625181

81782526025437

24491324422565

311892822741

1312513414838

60851393724220

661463325670

472251225472

88672470425279

67422162322745

147994824178

85222426124307

192022240624609.

In the first data processing device/method as described above, LDPC coding is performed on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rater of 9/15, group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits is performed, and the LDPC code is mapped into one of 1024 signal points determined according to a modulation scheme in units of 10 bits. In the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

18, 8, 166, 117, 4, 111, 142, 148, 176, 91, 120, 144, 99, 124, 20, 25, 31, 78, 36, 72, 2, 98, 93, 74, 174, 52, 152, 62, 88, 75, 23, 97, 147, 15, 71, 1, 127, 138, 81, 83, 68, 94, 112, 119, 121, 89, 163, 85, 86, 28, 17, 64, 14, 44, 158, 159, 150, 32, 128, 70, 90, 29, 30, 63, 100, 65, 129, 140, 177, 46, 84, 92, 10, 33, 58, 7, 96, 151, 171, 40, 76, 6, 3, 37, 104, 57, 135, 103, 141, 107, 116, 160, 41, 153, 175, 55, 130, 118, 131, 42, 27, 133, 95, 179, 34, 21, 87, 106, 105, 108, 79, 134, 113, 26, 164, 114, 73, 102, 77, 22, 110, 161, 43, 122, 123, 82, 5, 48, 139, 60, 49, 154, 115, 146, 67, 69, 137, 109, 143, 24, 101, 45, 16, 12, 19, 178, 80, 51, 47, 149, 50, 172, 170, 169, 61, 9, 39, 136, 59, 38, 54, 156, 126, 125, 145, 0, 13, 155, 132, 162, 11, 157, 66, 165, 173, 56, 168, 167, 53, and 35.

The LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079 17363 19374 19543 20530 22833 24339

271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 23938 25351 25590 25876 25910

73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600

1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177

1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913

28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336 23367 23890 24061 25657 25680

0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863

29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941 24137 24269 24416 24803 25154 25395

55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872

1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 25668 25679 25858 25888 25915

7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 25293 25403

48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 23990 24286 24409 24595 25802

12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 25463 25838

3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 22959 24768 24814 25594 25626 25880

21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 24431 25512 25814

18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 25547 25562 25733 25789 25906

4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20503 22228 24332 24613 25689 25855 25883

0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19665 20253 21996 24136 24890 25758 25784 25807

34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 24873 25107 25644

1595 6216 22850 25439

1562 15172 19517 22362

7508 12879 24324 24496

6298 15819 16757 18721

11173 15175 19966 21195

59 13505 16941 23793

2267 4830 12023 20587

8827 9278 13072 16664

14419 17463 23398 25348

6112 16534 20423 22698

493 8914 21103 24799

6896 12761 13206 25873

2 1380 12322 21701

11600 21306 25753 25790

8421 13076 14271 15401

9630 14112 19017 20955

212 13932 21781 25824

5961 9110 16654 19636

58 5434 9936 12770

6575 11433 19798

2731 7338 20926

14253 18463 25404

21791 24805 25869

2 11646 15850

6075 8586 23819

18435 22093 24852

2103 2368 11704

10925 17402 18232

9062 25061 25674

18497 20853 23404

18606 19364 19551

7 1022 25543

6744 15481 25868

9081 17305 25164

8 23701 25883

9680 19955 22848

56 4564 19121

5595 15086 25892

3174 17127 23183

19397 19817 20275

12561 24571 25825

7111 9889 25865

19104 20189 21851

549 9686 25548

6586 20325 25906

3224 20710 21637

641 15215 25754

13484 23729 25818

2043 7493 24246

16860 25230 25768

22047 24200 24902

9391 18040 19499

7855 24336 25069

23834 25570 25852

1977 8800 25756

6671 21772 25859

3279 6710 24444

24099 25117 25820

5553 12306 25915

48 11107 23907

10832 11974 25773

2223 17905 25484

16782 17135 20446

475 2861 3457

16218 22449 24362

11716 22200 25897

8315 15009 22633

13 20480 25852

12352 18658 25687

3681 14794 23703

30 24531 25846

4103 22077 24107

23837 25622 25812

3627 13387 25839

908 5367 19388

0 6894 25795

20322 23546 25181

8178 25260 25437

2449 13244 22565

31 18928 22741

1312 5134 14838

6085 13937 24220

66 14633 25670

47 22512 25472

8867 24704 25279

6742 21623 22745

147 9948 24178

8522 24261 24307

19202 22406 24609.

According to the present technology, there is provided a second data processing device/method including a group-wise deinterleaving unit/step that returns a sequence of the LDPC code after the group-wise interleave that is acquired from data transmitted from a transmitting device to an original state. The transmitting device includes: a coding unit that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 9/15; a group-wise interleaving unit that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

18, 8, 166, 117, 4, 111, 142, 148, 176, 91, 120, 144, 99, 124, 20, 25, 31, 78, 36, 72, 2, 98, 93, 74, 174, 52, 152, 62, 88, 75, 23, 97, 147, 15, 71, 1, 127, 138, 81, 83, 68, 94, 112, 119, 121, 89, 163, 85, 86, 28, 17, 64, 14, 44, 158, 159, 150, 32, 128, 70, 90, 29, 30, 63, 100, 65, 129, 140, 177, 46, 84, 92, 10, 33, 58, 7, 96, 151, 171, 40, 76, 6, 3, 37, 104, 57, 135, 103, 141, 107, 116, 160, 41, 153, 175, 55, 130, 118, 131, 42, 27, 133, 95, 179, 34, 21, 87, 106, 105, 108, 79, 134, 113, 26, 164, 114, 73, 102, 77, 22, 110, 161, 43, 122, 123, 82, 5, 48, 139, 60, 49, 154, 115, 146, 67, 69, 137, 109, 143, 24, 101, 45, 16, 12, 19, 178, 80, 51, 47, 149, 50, 172, 170, 169, 61, 9, 39, 136, 59, 38, 54, 156, 126, 125, 145, 0, 13, 155, 132, 162, 11, 157, 66, 165, 173, 56, 168, 167, 53, and 35,

the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079 17363 19374 19543 20530 22833 24339

271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 23938 25351 25590 25876 25910

73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600

1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177

1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913

28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336 23367 23890 24061 25657 25680

0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863

29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941 24137 24269 24416 24803 25154 25395

55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872

1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 25668 25679 25858 25888 25915

7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 25293 25403

48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 23990 24286 24409 24595 25802

12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 25463 25838

3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 22959 24768 24814 25594 25626 25880

21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 24431 25512 25814

18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 25547 25562 25733 25789 25906

4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20503 22228 24332 24613 25689 25855 25883

0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19665 20253 21996 24136 24890 25758 25784 25807

34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 24873 25107 25644

1595 6216 22850 25439

1562 15172 19517 22362

7508 12879 24324 24496

6298 15819 16757 18721

11173 15175 19966 21195

59 13505 16941 23793

2267 4830 12023 20587

8827 9278 13072 16664

14419 17463 23398 25348

6112 16534 20423 22698

493 8914 21103 24799

6896 12761 13206 25873

2 1380 12322 21701

11600 21306 25753 25790

8421 13076 14271 15401

9630 14112 19017 20955

212 13932 21781 25824

5961 9110 16654 19636

58 5434 9936 12770

6575 11433 19798

2731 7338 20926

14253 18463 25404

21791 24805 25869

2 11646 15850

6075 8586 23819

18435 22093 24852

2103 2368 11704

10925 17402 18232

9062 25061 25674

18497 20853 23404

18606 19364 19551

7 1022 25543

6744 15481 25868

9081 17305 25164

8 23701 25883

9680 19955 22848

56 4564 19121

5595 15086 25892

3174 17127 23183

19397 19817 20275

12561 24571 25825

7111 9889 25865

19104 20189 21851

549 9686 25548

6586 20325 25906

3224 20710 21637

641 15215 25754

13484 23729 25818

2043 7493 24246

16860 25230 25768

22047 24200 24902

9391 18040 19499

7855 24336 25069

23834 25570 25852

1977 8800 25756

6671 21772 25859

3279 6710 24444

24099 25117 25820

5553 12306 25915

48 11107 23907

10832 11974 25773

2223 17905 25484

16782 17135 20446

475 2861 3457

16218 22449 24362

11716 22200 25897

8315 15009 22633

13 20480 25852

12352 18658 25687

3681 14794 23703

30 24531 25846

4103 22077 24107

23837 25622 25812

3627 13387 25839

908 5367 19388

0 6894 25795

20322 23546 25181

8178 25260 25437

2449 13244 22565

31 18928 22741

1312 5134 14838

6085 13937 24220

66 14633 25670

47 22512 25472

8867 24704 25279

6742 21623 22745

147 9948 24178

8522 24261 24307

19202 22406 24609.

In the second data processing device/method as above, a sequence of the LDPC code after the group-wise interleave that is acquired from data transmitted from a transmitting device is returned to an original state, wherein the transmitting device includes: a coding unit that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 9/15; a group-wise interleaving unit that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

18, 8, 166, 117, 4, 111, 142, 148, 176, 91, 120, 144, 99, 124, 20, 25, 31, 78, 36, 72, 2, 98, 93, 74, 174, 52, 152, 62, 88, 75, 23, 97, 147, 15, 71, 1, 127, 138, 81, 83, 68, 94, 112, 119, 121, 89, 163, 85, 86, 28, 17, 64, 14, 44, 158, 159, 150, 32, 128, 70, 90, 29, 30, 63, 100, 65, 129, 140, 177, 46, 84, 92, 10, 33, 58, 7, 96, 151, 171, 40, 76, 6, 3, 37, 104, 57, 135, 103, 141, 107, 116, 160, 41, 153, 175, 55, 130, 118, 131, 42, 27, 133, 95, 179, 34, 21, 87, 106, 105, 108, 79, 134, 113, 26, 164, 114, 73, 102, 77, 22, 110, 161, 43, 122, 123, 82, 5, 48, 139, 60, 49, 154, 115, 146, 67, 69, 137, 109, 143, 24, 101, 45, 16, 12, 19, 178, 80, 51, 47, 149, 50, 172, 170, 169, 61, 9, 39, 136, 59, 38, 54, 156, 126, 125, 145, 0, 13, 155, 132, 162, 11, 157, 66, 165, 173, 56, 168, 167, 53, and 35,

the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079 17363 19374 19543 20530 22833 24339

271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 23938 25351 25590 25876 25910

73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600

1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177

1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913

28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336 23367 23890 24061 25657 25680

0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863

29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941 24137 24269 24416 24803 25154 25395

55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872

1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 25668 25679 25858 25888 25915

7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 25293 25403

48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 23990 24286 24409 24595 25802

12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 25463 25838

3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 22959 24768 24814 25594 25626 25880

21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 24431 25512 25814

18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 25547 25562 25733 25789 25906

4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20503 22228 24332 24613 25689 25855 25883

0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19665 20253 21996 24136 24890 25758 25784 25807

34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 24873 25107 25644

1595 6216 22850 25439

1562 15172 19517 22362

7508 12879 24324 24496

6298 15819 16757 18721

11173 15175 19966 21195

59 13505 16941 23793

2267 4830 12023 20587

8827 9278 13072 16664

14419 17463 23398 25348

6112 16534 20423 22698

493 8914 21103 24799

6896 12761 13206 25873

2 1380 12322 21701

11600 21306 25753 25790

8421 13076 14271 15401

9630 14112 19017 20955

212 13932 21781 25824

5961 9110 16654 19636

58 5434 9936 12770

6575 11433 19798

2731 7338 20926

14253 18463 25404

21791 24805 25869

2 11646 15850

6075 8586 23819

18435 22093 24852

2103 2368 11704

10925 17402 18232

9062 25061 25674

18497 20853 23404

18606 19364 19551

7 1022 25543

6744 15481 25868

9081 17305 25164

8 23701 25883

9680 19955 22848

56 4564 19121

5595 15086 25892

3174 17127 23183

19397 19817 20275

12561 24571 25825

7111 9889 25865

19104 20189 21851

549 9686 25548

6586 20325 25906

3224 20710 21637

641 15215 25754

13484 23729 25818

2043 7493 24246

16860 25230 25768

22047 24200 24902

9391 18040 19499

7855 24336 25069

23834 25570 25852

1977 8800 25756

6671 21772 25859

3279 6710 24444

24099 25117 25820

5553 12306 25915

48 11107 23907

10832 11974 25773

2223 17905 25484

16782 17135 20446

475 2861 3457

16218 22449 24362

11716 22200 25897

8315 15009 22633

13 20480 25852

12352 18658 25687

3681 14794 23703

30 24531 25846

4103 22077 24107

23837 25622 25812

3627 13387 25839

908 5367 19388

0 6894 25795

20322 23546 25181

8178 25260 25437

2449 13244 22565

31 18928 22741

1312 5134 14838

6085 13937 24220

66 14633 25670

47 22512 25472

8867 24704 25279

6742 21623 22745

147 9948 24178

8522 24261 24307

19202 22406 24609.

According to the present technology, there is provided a third data processing device/method including: a coding unit/step that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 11/15; a group-wise interleaving unit/step that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit/step that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

51, 47, 53, 43, 55, 59, 49, 33, 35, 31, 24, 37, 0, 2, 45, 41, 39, 57, 42, 44, 52, 40, 23, 30, 32, 34, 54, 56, 46, 50, 122, 48, 1, 36, 38, 58, 77, 3, 65, 81, 67, 147, 83, 69, 26, 75, 85, 73, 79, 145, 71, 63, 5, 61, 70, 78, 68, 62, 66, 6, 64, 149, 60, 82, 80, 4, 76, 84, 72, 154, 86, 74, 89, 128, 137, 91, 141, 93, 101, 7, 87, 9, 103, 99, 95, 11, 13, 143, 97, 133, 136, 12, 100, 94, 14, 88, 142, 96, 92, 8, 152, 10, 139, 102, 104, 132, 90, 98, 114, 112, 146, 123, 110, 15, 125, 150, 120, 153, 29, 106, 134, 27, 127, 108, 130, 116, 28, 107, 126, 25, 131, 124, 129, 151, 121, 105, 111, 115, 135, 148, 109, 117, 158, 113, 170, 119, 162, 178, 155, 176, 18, 20, 164, 157, 160, 22, 140, 16, 168, 166, 172, 174, 175, 179, 118, 138, 156, 19, 169, 167, 163, 173, 161, 177, 165, 144, 171, 17, 21, and 159,

the LDPC code includes information bits and parity bits, the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226

1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103

40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255.

In the third data processing device/method as described above, LDPC coding is performed on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 11/15, group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits is performed, and the LDPC code is mapped into one of 1024 signal points determined according to a modulation scheme in units of 10 bits. In the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

51, 47, 53, 43, 55, 59, 49, 33, 35, 31, 24, 37, 0, 2, 45, 41, 39, 57, 42, 44, 52, 40, 23, 30, 32, 34, 54, 56, 46, 50, 122, 48, 1, 36, 38, 58, 77, 3, 65, 81, 67, 147, 83, 69, 26, 75, 85, 73, 79, 145, 71, 63, 5, 61, 70, 78, 68, 62, 66, 6, 64, 149, 60, 82, 80, 4, 76, 84, 72, 154, 86, 74, 89, 128, 137, 91, 141, 93, 101, 7, 87, 9, 103, 99, 95, 11, 13, 143, 97, 133, 136, 12, 100, 94, 14, 88, 142, 96, 92, 8, 152, 10, 139, 102, 104, 132, 90, 98, 114, 112, 146, 123, 110, 15, 125, 150, 120, 153, 29, 106, 134, 27, 127, 108, 130, 116, 28, 107, 126, 25, 131, 124, 129, 151, 121, 105, 111, 115, 135, 148, 109, 117, 158, 113, 170, 119, 162, 178, 155, 176, 18, 20, 164, 157, 160, 22, 140, 16, 168, 166, 172, 174, 175, 179, 118, 138, 156, 19, 169, 167, 163, 173, 161, 177, 165, 144, 171, 17, 21, and 159.

The LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226

1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103

40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255.

According to the present technology, there is provided a fourth data processing device/method including a group-wise deinterleaving unit/step that returns a sequence of the LDPC code after the group-wise interleave that is acquired from data transmitted from a transmitting device to an original state. The transmitting device includes: a coding unit that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 11/15; a group-wise interleaving unit that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

51, 47, 53, 43, 55, 59, 49, 33, 35, 31, 24, 37, 0, 2, 45, 41, 39, 57, 42, 44, 52, 40, 23, 30, 32, 34, 54, 56, 46, 50, 122, 48, 1, 36, 38, 58, 77, 3, 65, 81, 67, 147, 83, 69, 26, 75, 85, 73, 79, 145, 71, 63, 5, 61, 70, 78, 68, 62, 66, 6, 64, 149, 60, 82, 80, 4, 76, 84, 72, 154, 86, 74, 89, 128, 137, 91, 141, 93, 101, 7, 87, 9, 103, 99, 95, 11, 13, 143, 97, 133, 136, 12, 100, 94, 14, 88, 142, 96, 92, 8, 152, 10, 139, 102, 104, 132, 90, 98, 114, 112, 146, 123, 110, 15, 125, 150, 120, 153, 29, 106, 134, 27, 127, 108, 130, 116, 28, 107, 126, 25, 131, 124, 129, 151, 121, 105, 111, 115, 135, 148, 109, 117, 158, 113, 170, 119, 162, 178, 155, 176, 18, 20, 164, 157, 160, 22, 140, 16, 168, 166, 172, 174, 175, 179, 118, 138, 156, 19, 169, 167, 163, 173, 161, 177, 165, 144, 171, 17, 21, and 159,

the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226

1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103

40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255.

In the fourth data processing device/method as above, a sequence of the LDPC code after the group-wise interleave that is acquired from data transmitted from a transmitting device is returned to an original state, wherein the transmitting device includes: a coding unit that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 11/15; a group-wise interleaving unit that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

51, 47, 53, 43, 55, 59, 49, 33, 35, 31, 24, 37, 0, 2, 45, 41, 39, 57, 42, 44, 52, 40, 23, 30, 32, 34, 54, 56, 46, 50, 122, 48, 1, 36, 38, 58, 77, 3, 65, 81, 67, 147, 83, 69, 26, 75, 85, 73, 79, 145, 71, 63, 5, 61, 70, 78, 68, 62, 66, 6, 64, 149, 60, 82, 80, 4, 76, 84, 72, 154, 86, 74, 89, 128, 137, 91, 141, 93, 101, 7, 87, 9, 103, 99, 95, 11, 13, 143, 97, 133, 136, 12, 100, 94, 14, 88, 142, 96, 92, 8, 152, 10, 139, 102, 104, 132, 90, 98, 114, 112, 146, 123, 110, 15, 125, 150, 120, 153, 29, 106, 134, 27, 127, 108, 130, 116, 28, 107, 126, 25, 131, 124, 129, 151, 121, 105, 111, 115, 135, 148, 109, 117, 158, 113, 170, 119, 162, 178, 155, 176, 18, 20, 164, 157, 160, 22, 140, 16, 168, 166, 172, 174, 175, 179, 118, 138, 156, 19, 169, 167, 163, 173, 161, 177, 165, 144, 171, 17, 21, and 159,

the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912

444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268

401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157

1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205

542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063

17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226

1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241

15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209

0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237

3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090

981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953

1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273

1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262

2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247

1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195

2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263

3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123

26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103

40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266

904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259

7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253

4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204

24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220

88 11622 14705 15890

304 2026 2638 6018

1163 4268 11620 17232

9701 11785 14463 17260

4118 10952 12224 17006

3647 10823 11521 12060

1717 3753 9199 11642

2187 14280 17220

14787 16903 17061

381 3534 4294

3149 6947 8323

12562 16724 16881

7289 9997 15306

5615 13152 17260

5666 16926 17027

4190 7798 16831

4778 10629 17180

10001 13884 15453

6 2237 8203

7831 15144 15160

9186 17204 17243

9435 17168 17237

42 5701 17159

7812 14259 15715

39 4513 6658

38 9368 11273

1119 4785 17182

5620 16521 16729

16 6685 17242

210 3452 12383

466 14462 16250

10548 12633 13962

1452 6005 16453

22 4120 13684

5195 11563 16522

5518 16705 17201

12233 14552 15471

6067 13440 17248

8660 8967 17061

8673 12176 15051

5959 15767 16541

3244 12109 12414

31 15913 16323

3270 15686 16653

24 7346 14675

12 1531 8740

6228 7565 16667

16936 17122 17162

4868 8451 13183

3714 4451 16919

11313 13801 17132

17070 17191 17242

1911 11201 17186

14 17190 17254

11760 16008 16832

14543 17033 17278

16129 16765 17155

6891 15561 17007

12741 14744 17116

8992 16661 17277

1861 11130 16742

4822 13331 16192

13281 14027 14989

38 14887 17141

10698 13452 15674

4 2539 16877

857 17170 17249

11449 11906 12867

285 14118 16831

15191 17214 17242

39 728 16915

2469 12969 15579

16644 17151 17164

2592 8280 10448

9236 12431 17173

9064 16892 17233

4526 16146 17038

31 2116 16083

15837 16951 17031

5362 8382 16618

6137 13199 17221

2841 15068 17068

24 3620 17003

9880 15718 16764

1784 10240 17209

2731 10293 10846

3121 8723 16598

8563 15662 17088

13 1167 14676

29 13850 15963

3654 7553 8114

23 4362 14865

4434 14741 16688

8362 13901 17244

13687 16736 17232

46 4229 13394

13169 16383 16972

16031 16681 16952

3384 9894 12580

9841 14414 16165

5013 17099 17115

2130 8941 17266

6907 15428 17241

16 1860 17235

2151 16014 16643

14954 15958 17222

3969 8419 15116

31 15593 16984

11514 16605 17255.

According to the present technology, there is provided a fifth data processing device/method including: a coding unit/step that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 13/15; a group-wise interleaving unit/step that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit/step that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175,

the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

142 2307 2598 2650 4028 4434 5781 5881 6016 6323 6681 6698 8125

2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 8539 8583

899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602

21 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616

20 1745 2838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631

9 6274 6725 6792 7195 7333 8027 8186 8209 8273 8442 8548 8632

494 1365 2405 3799 5188 5291 7644 7926 8139 8458 8504 8594 8625

192 574 1179 4387 4695 5089 5831 7673 7789 8298 8301 8612 8632

11 20 1406 6111 6176 6256 6708 6834 7828 8232 8457 8495 8602

6 2654 3554 4483 4966 5866 6795 8069 8249 8301 8497 8509 8623

21 1144 2355 3124 6773 6805 6887 7742 7994 8358 8374 8580 8611

335 4473 4883 5528 6096 7543 7586 7921 8197 8319 8394 8489 8636

2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 8544 8586 8617

12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 8137

710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619

200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526

3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636

3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598

105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587

787 1857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537

15 1118 4226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568

36 5216 5368 5616 6029 6591 8038 8067 8299 8351 8565 8578 8585

1 23 4300 4530 5426 5532 5817 6967 7124 7979 8022 8270 8437

629 2133 4828 5475 5875 5890 7194 8042 8345 8385 8518 8598 8612

11 1065 3782 4237 4993 7104 7863 7904 8104 8228 8321 8383 8565

2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 8527 8557 8614

5600 6591 7491 7696

1766 8281 8626

1725 2280 5120

1650 3445 7652

4312 6911 8626

15 1013 5892

2263 2546 2979

1545 5873 7406

67 726 3697

2860 6443 8542

17 911 2820

1561 4580 6052

79 5269 7134

22 2410 2424

3501 5642 8627

808 6950 8571

4099 6389 7482

4023 5000 7833

5476 5765 7917

1008 3194 7207

20 495 5411

1703 8388 8635

6 4395 4921

200 2053 8206

1089 5126 5562

10 4193 7720

1967 2151 4608

22 738 3513

3385 5066 8152

440 1118 8537

3429 6058 7716

5213 7519 8382

5564 8365 8620

43 3219 8603

4 5409 5815

5 6376 7654

4091 5724 5953

5348 6754 8613

1634 6398 6632

72 2058 8605

3497 5811 7579

3846 6743 8559

15 5933 8629

2133 5859 7068

4151 4617 8566

2960 8270 8410

2059 3617 8210

544 1441 6895

4043 7482 8592

294 2180 8524

3058 8227 8373

364 5756 8617

5383 8555 8619

1704 2480 4181

7338 7929 7990

2615 3905 7981

4298 4548 8296

8262 8319 8630

892 1893 8028

5694 7237 8595

1487 5012 5810

4335 8593 8624

3509 4531 5273

10 22 830

4161 5208 6280

275 7063 8634

4 2725 3113

2279 7403 8174

1637 3328 3930

2810 4939 5624

3 1234 7687

2799 7740 8616

22 7701 8636

4302 7857 7993

7477 7794 8592

9 6111 8591

5 8606 8628

347 3497 4033

1747 2613 8636

1827 5600 7042

580 1822 6842

232 7134 7783

4629 5000 7231

951 2806 4947

571 3474 8577

2437 2496 7945

23 5873 8162

12 1168 7686

8315 8540 8596

1766 2506 4733

929 1516 3338

21 1216 6555

782 1452 8617

8 6083 6087

667 3240 4583

4030 4661 5790

559 7122 8553

3202 4388 4909

2533 3673 8594

1991 3954 6206

6835 7900 7980

189 5722 8573

2680 4928 4998

243 2579 7735

4281 8132 8566

7656 7671 8609

1116 2291 4166

21 388 8021

6 1123 8369

311 4918 8511

0 3248 6290

13 6762 7172

4209 5632 7563

49 127 8074

581 1735 4075

0 2235 5470

2178 5820 6179

16 3575 6054

1095 4564 6458

9 1581 5953

2537 6469 8552

14 3874 4844

0 3269 3551

2114 7372 7926

1875 2388 4057

3232 4042 6663

9 401 583

13 4100 6584

2299 4190 4410

21 3670 4979.

In the fifth data processing device/method as described above, LDPC coding is performed on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 13/15, group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits is performed, and the LDPC code is mapped into one of 1024 signal points determined according to a modulation scheme in units of 10 bits. In the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175.

The LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

142 2307 2598 2650 4028 4434 5781 5881 6016 6323 6681 6698 8125

2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 8539 8583

899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602

21 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616

20 1745 2838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631

9 6274 6725 6792 7195 7333 8027 8186 8209 8273 8442 8548 8632

494 1365 2405 3799 5188 5291 7644 7926 8139 8458 8504 8594 8625

192 574 1179 4387 4695 5089 5831 7673 7789 8298 8301 8612 8632

11 20 1406 6111 6176 6256 6708 6834 7828 8232 8457 8495 8602

6 2654 3554 4483 4966 5866 6795 8069 8249 8301 8497 8509 8623

21 1144 2355 3124 6773 6805 6887 7742 7994 8358 8374 8580 8611

335 4473 4883 5528 6096 7543 7586 7921 8197 8319 8394 8489 8636

2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 8544 8586 8617

12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 8137

710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619

200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526

3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636

3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598

105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587

787 1857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537

15 1118 4226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568

36 5216 5368 5616 6029 6591 8038 8067 8299 8351 8565 8578 8585

1 23 4300 4530 5426 5532 5817 6967 7124 7979 8022 8270 8437

629 2133 4828 5475 5875 5890 7194 8042 8345 8385 8518 8598 8612

11 1065 3782 4237 4993 7104 7863 7904 8104 8228 8321 8383 8565

2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 8527 8557 8614

5600 6591 7491 7696

1766 8281 8626

1725 2280 5120

1650 3445 7652

4312 6911 8626

15 1013 5892

2263 2546 2979

1545 5873 7406

67 726 3697

2860 6443 8542

17 911 2820

1561 4580 6052

79 5269 7134

22 2410 2424

3501 5642 8627

808 6950 8571

4099 6389 7482

4023 5000 7833

5476 5765 7917

1008 3194 7207

20 495 5411

1703 8388 8635

6 4395 4921

200 2053 8206

1089 5126 5562

10 4193 7720

1967 2151 4608

22 738 3513

3385 5066 8152

440 1118 8537

3429 6058 7716

5213 7519 8382

5564 8365 8620

43 3219 8603

4 5409 5815

5 6376 7654

4091 5724 5953

5348 6754 8613

1634 6398 6632

72 2058 8605

3497 5811 7579

3846 6743 8559

15 5933 8629

2133 5859 7068

4151 4617 8566

2960 8270 8410

2059 3617 8210

544 1441 6895

4043 7482 8592

294 2180 8524

3058 8227 8373

364 5756 8617

5383 8555 8619

1704 2480 4181

7338 7929 7990

2615 3905 7981

4298 4548 8296

8262 8319 8630

892 1893 8028

5694 7237 8595

1487 5012 5810

4335 8593 8624

3509 4531 5273

10 22 830

4161 5208 6280

275 7063 8634

4 2725 3113

2279 7403 8174

1637 3328 3930

2810 4939 5624

3 1234 7687

2799 7740 8616

22 7701 8636

4302 7857 7993

7477 7794 8592

9 6111 8591

5 8606 8628

347 3497 4033

1747 2613 8636

1827 5600 7042

580 1822 6842

232 7134 7783

4629 5000 7231

951 2806 4947

571 3474 8577

2437 2496 7945

23 5873 8162

12 1168 7686

8315 8540 8596

1766 2506 4733

929 1516 3338

21 1216 6555

782 1452 8617

8 6083 6087

667 3240 4583

4030 4661 5790

559 7122 8553

3202 4388 4909

2533 3673 8594

1991 3954 6206

6835 7900 7980

189 5722 8573

2680 4928 4998

243 2579 7735

4281 8132 8566

7656 7671 8609

1116 2291 4166

21 388 8021

6 1123 8369

311 4918 8511

0 3248 6290

13 6762 7172

4209 5632 7563

49 127 8074

581 1735 4075

0 2235 5470

2178 5820 6179

16 3575 6054

1095 4564 6458

9 1581 5953

2537 6469 8552

14 3874 4844

0 3269 3551

2114 7372 7926

1875 2388 4057

3232 4042 6663

9 401 583

13 4100 6584

2299 4190 4410

21 3670 4979.

According to the present technology, there is provided a sixth data processing device/method including a group-wise deinterleaving unit/step that returns a sequence of the LDPC code after the group-wise interleave that is acquired from data transmitted from a transmitting device to an original state. The transmitting device includes: a coding unit that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 13/15; a group-wise interleaving unit that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175,

the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

142 2307 2598 2650 4028 4434 5781 5881 6016 6323 6681 6698 8125

2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 8539 8583

899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602

21 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616

20 1745 2838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631

9 6274 6725 6792 7195 7333 8027 8186 8209 8273 8442 8548 8632

494 1365 2405 3799 5188 5291 7644 7926 8139 8458 8504 8594 8625

192 574 1179 4387 4695 5089 5831 7673 7789 8298 8301 8612 8632

11 20 1406 6111 6176 6256 6708 6834 7828 8232 8457 8495 8602

6 2654 3554 4483 4966 5866 6795 8069 8249 8301 8497 8509 8623

21 1144 2355 3124 6773 6805 6887 7742 7994 8358 8374 8580 8611

335 4473 4883 5528 6096 7543 7586 7921 8197 8319 8394 8489 8636

2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 8544 8586 8617

12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 8137

710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619

200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526

3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636

3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598

105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587

787 1857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537

15 1118 4226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568

36 5216 5368 5616 6029 6591 8038 8067 8299 8351 8565 8578 8585

1 23 4300 4530 5426 5532 5817 6967 7124 7979 8022 8270 8467

629 2133 4828 5475 5875 5890 7194 8042 8345 8385 8518 8598 8612

11 1065 3782 4237 4993 7104 7863 7904 8104 8228 8321 8383 8565

2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 8527 8557 8614

5600 6591 7491 7696

1766 8281 8626

1725 2280 5120

1650 3445 7652

4312 6911 8626

15 1013 5892

2263 2546 2979

1545 5873 7406

67 726 3697

2860 6443 8542

17 911 2820

1561 4580 6052

79 5269 7134

22 2410 2424

3501 5642 8627

808 6950 8571

4099 6389 7482

4023 5000 7833

5476 5765 7917

1008 3194 7207

20 495 5411

1703 8388 8635

6 4395 4921

200 2053 8206

1089 5126 5562

10 4193 7720

1967 2151 4608

22 738 3513

3385 5066 8152

440 1118 8537

3429 6058 7716

5213 7519 8382

5564 8365 8620

43 3219 8603

4 5409 5815

5 6376 7654

4091 5724 5953

5348 6754 8613

1634 6398 6632

72 2058 8605

3497 5811 7579

3846 6743 8559

15 5933 8629

2133 5859 7068

4151 4617 8566

2960 8270 8410

2059 3617 8210

544 1441 6895

4043 7482 8592

294 2180 8524

3058 8227 8373

364 5756 8617

5383 8555 8619

1704 2480 4181

7338 7929 7990

2615 3905 7981

4298 4548 8296

8262 8319 8630

892 1893 8028

5694 7237 8595

1487 5012 5810

4335 8593 8624

3509 4531 5273

10 22 830

4161 5208 6280

275 7063 8634

4 2725 3113

2279 7403 8174

1637 3328 3930

2810 4939 5624

3 1234 7687

2799 7740 8616

22 7701 8636

4302 7857 7993

7477 7794 8592

9 6111 8591

5 8606 8628

347 3497 4033

1747 2613 8636

1827 5600 7042

580 1822 6842

232 7134 7783

4629 5000 7231

951 2806 4947

571 3474 8577

2437 2496 7945

23 5873 8162

12 1168 7686

8315 8540 8596

1766 2506 4733

929 1516 3338

21 1216 6555

782 1452 8617

8 6083 6087

667 3240 4583

4030 4661 5790

559 7122 8553

3202 4388 4909

2533 3673 8594

1991 3954 6206

6835 7900 7980

189 5722 8573

2680 4928 4998

243 2579 7735

4281 8132 8566

7656 7671 8609

1116 2291 4166

21 388 8021

6 1123 8369

311 4918 8511

0 3248 6290

13 6762 7172

4209 5632 7563

49 127 8074

581 1735 4075

0 2235 5470

2178 5820 6179

16 3575 6054

1095 4564 6458

9 1581 5953

2537 6469 8552

14 3874 4844

0 3269 3551

2114 7372 7926

1875 2388 4057

3232 4042 6663

9 401 583

13 4100 6584

2299 4190 4410

21 3670 4979.

In the sixth data processing device/method as above, a sequence of the LDPC code after the group-wise interleave that is acquired from data transmitted from a transmitting device is returned to an original state, wherein the transmitting device includes: a coding unit that performs LDPC coding on the basis of a parity check matrix of an LDPC code having a code length N of 64800 bits and a coding rate r of 13/15; a group-wise interleaving unit that performs group-wise interleave interleaving the LDPC code in units of bit groups of 360 bits; and a mapping unit that maps the LDPC code into one of 1024 signal points determined according to a modulation scheme in units of 10 bits, wherein, in the group-wise interleave, by using an (i+1)-th bit group from a head of the LDPC code as a bit group i, a sequence of bit groups 0 to 179 of the LDPC code of 64800 bits is interleaved into a sequence of bit groups

49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175,

the LDPC code includes information bits and parity bits, the parity check matrix includes an information matrix portion corresponding to the information bits and a parity matrix portion corresponding to the parity bits, the information matrix portion is represented by a parity check matrix initial value table, and the parity check matrix initial value table is a table representing a position of an element “1” in the information matrix portion for every 360 columns and is

142 2307 2598 2650 4028 4434 5781 5881 6016 6323 6681 6698 8125

2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 8539 8583

899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602

21 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616

20 1745 2838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631

9 6274 6725 6792 7195 7333 8027 8186 8209 8273 8442 8548 8632

494 1365 2405 3799 5188 5291 7644 7926 8139 8458 8504 8594 8625

192 574 1179 4387 4695 5089 5831 7673 7789 8298 8301 8612 8632

11 20 1406 6111 6176 6256 6708 6834 7828 8232 8457 8495 8602

6 2654 3554 4483 4966 5866 6795 8069 8249 8301 8497 8509 8623

21 1144 2355 3124 6773 6805 6887 7742 7994 8358 8374 8580 8611

335 4473 4883 5528 6096 7543 7586 7921 8197 8319 8394 8489 8636

2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 8544 8586 8617

12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 8137

710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619

200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526

3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636

3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598

105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587

787 1857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537

15 1118 4226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568

36 5216 5368 5616 6029 6591 8038 8067 8299 8351 8565 8578 8585

1 23 4300 4530 5426 5532 5817 6967 7124 7979 8022 8270 8437

629 2133 4828 5475 5875 5890 7194 8042 8345 8385 8518 8598 8612

11 1065 3782 4237 4993 7104 7863 7904 8104 8228 8321 8383 8565

2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 8527 8557 8614

5600 6591 7491 7696

1766 8281 8626

1725 2280 5120

1650 3445 7652

4312 6911 8626

15 1013 5892

2263 2546 2979

1545 5873 7406

67 726 3697

2860 6443 8542

17 911 2820

1561 4580 6052

79 5269 7134

22 2410 2424

3501 5642 8627

808 6950 8571

4099 6389 7482

4023 5000 7833

5476 5765 7917

1008 3194 7207

20 495 5411

1703 8388 8635

6 4395 4921

200 2053 8206

1089 5126 5562

10 4193 7720

1967 2151 4608

22 738 3513

3385 5066 8152

440 1118 8537

3429 6058 7716

5213 7519 8382

5564 8365 8620

43 3219 8603

4 5409 5815

5 6376 7654

4091 5724 5953

5348 6754 8613

1634 6398 6632

72 2058 8605

3497 5811 7579

3846 6743 8559

15 5933 8629

2133 5859 7068

4151 4617 8566

2960 8270 8410

2059 3617 8210

544 1441 6895

4043 7482 8592

294 2180 8524

3058 8227 8373

364 5756 8617

5383 8555 8619

1704 2480 4181

7338 7929 7990

2615 3905 7981

4298 4548 8296

8262 8319 8630

892 1893 8028

5694 7237 8595

1487 5012 5810

4335 8593 8624

3509 4531 5273

10 22 830

4161 5208 6280

275 7063 8634

4 2725 3113

2279 7403 8174

1637 3328 3930

2810 4939 5624

3 1234 7687

2799 7740 8616

22 7701 8636

4302 7857 7993

7477 7794 8592

9 6111 8591

5 8606 8628

347 3497 4033

1747 2613 8636

1827 5600 7042

580 1822 6842

232 7134 7783

4629 5000 7231

951 2806 4947

571 3474 8577

2437 2496 7945

23 5873 8162

12 1168 7686

8315 8540 8596

1766 2506 4733

929 1516 3338

21 1216 6555

782 1452 8617

8 6083 6087

667 3240 4583

4030 4661 5790

559 7122 8553

3202 4388 4909

2533 3673 8594

1991 3954 6206

6835 7900 7980

189 5722 8573

2680 4928 4998

243 2579 7735

4281 8132 8566

7656 7671 8609

1116 2291 4166

21 388 8021

6 1123 8369

311 4918 8511

0 3248 6290

13 6762 7172

4209 5632 7563

49 127 8074

581 1735 4075

0 2235 5470

2178 5820 6179

16 3575 6054

1095 4564 6458

9 1581 5953

2537 6469 8552

14 3874 4844

0 3269 3551

2114 7372 7926

1875 2388 4057

3232 4042 6663

9 401 583

13 4100 6584

2299 4190 4410

21 3670 4979.

Here, the data processing device may be an independent device or an internal block configuring one device.

Effects of the Invention

According to the present technology, in data transmission using the LDPC code, excellent communication quality can be secured.

Note that the effects described here are not necessarily limited, but anyone effect described in the present disclosure may be acquired.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram that illustrates a parity check matrix H of an LDPC code.

FIG. 2 is a flowchart that illustrates a decoding sequence of an LDPC code.

FIG. 3 is a diagram that illustrates an example of a parity check matrix of an LDPC code.

FIG. 4 is a diagram that illustrates an example of a Tanner graph of a parity check matrix.

FIG. 5 is a diagram that illustrates an example of a variable node.

FIG. 6 is a diagram that illustrates an example of a check node.

FIG. 7 is a diagram that illustrates a configuration example of a transmission system according to an embodiment of the present technology.

FIG. 8 is a block diagram that illustrates a configuration example of a transmitting device 11.

FIG. 9 is a block diagram that illustrates a configuration example of a bit interleaver 116.

FIG. 10 is a diagram that illustrates an example of a parity check matrix.

FIG. 11 is a diagram that illustrates an example of a parity matrix.

FIG. 12 is a diagram that illustrates the parity check matrix of the LDPC code that is defined in the standard of the DVB-T.2.

FIG. 13 is a diagram that illustrates the parity check matrix of the LDPC code that is defined in the standard of the DVB-T.2.

FIG. 14 is a diagram that illustrates an example of a Tanner graph for decoding an LDPC code.

FIG. 15 is a diagram that illustrates an example of a parity matrix H_(T) having a staircase structure and a Tanner graph corresponding to the parity matrix H_(T).

FIG. 16 is a diagram that illustrates an example of a parity matrix H_(T) of a parity check matrix H corresponding to an LDPC code after parity interleave.

FIG. 17 is a flowchart that illustrates an example of a process performed by a bit interleaver 116 and a mapper 117.

FIG. 18 is a block diagram that illustrates a configuration example of an LDPC encoder 115.

FIG. 19 is a flowchart that illustrates an example of the process of the LDPC encoder 115.

FIG. 20 is a diagram that illustrates an example of a parity check matrix initial value table in which a coding rate is 1/4 and a code length is 16200.

FIG. 21 is a diagram that illustrates a method of calculating a parity check matrix H by using a parity check matrix initial value table.

FIG. 22 is a diagram that illustrates a structure of a parity check matrix.

FIG. 23 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 24 is a diagram that illustrates an A matrix generated from a parity check matrix initial value table.

FIG. 25 is a diagram that illustrates parity interleave of a B matrix.

FIG. 26 is a diagram that illustrates a C matrix generated from a parity check matrix initial value table.

FIG. 27 is a diagram that illustrates parity interleave of a D matrix.

FIG. 28 is a diagram that illustrates a parity check matrix acquired by performing a column permutation as parity deinterleave for restoring parity interleave to an original state for a parity check matrix.

FIG. 29 is a diagram that illustrates a transformed parity check matrix acquired by performing a row permutation for a parity check matrix.

FIG. 30 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 31 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 32 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 33 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 34 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 35 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 36 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 37 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 38 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 39 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 40 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 41 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 42 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 43 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 44 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 45 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 46 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 47 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 48 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 49 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 50 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 51 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 52 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 53 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 54 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 55 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 56 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 57 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 58 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 59 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 60 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 61 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 62 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 63 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 64 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 65 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 66 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 67 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 68 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 69 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 70 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 71 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 72 is a diagram that illustrates an example of the parity check matrix initial value table.

FIG. 73 is a diagram that illustrates an example of a Tanner graph of an ensemble of a degree sequence in which a column weight is 3, and a row weight is 6.

FIG. 74 is a diagram that illustrates an example of a Tanner graph of an ensemble of a multi-edge type.

FIG. 75 is a diagram that illustrates a parity check matrix.

FIG. 76 is a diagram that illustrates a parity check matrix.

FIG. 77 is a diagram that illustrates a parity check matrix.

FIG. 78 is a diagram that illustrates a parity check matrix.

FIG. 79 is a diagram that illustrates a parity check matrix.

FIG. 80 is a diagram that illustrates a parity check matrix.

FIG. 81 is a diagram that illustrates a parity check matrix.

FIG. 82 is a diagram that illustrates a parity check matrix.

FIG. 83 is a diagram that illustrates an example of a constellation in a case where a modulation scheme is 16 QAM.

FIG. 84 is a diagram that illustrates an example of a constellation in a case where a modulation scheme is 64 QAM.

FIG. 85 is a diagram that illustrates an example of a constellation in a case where a modulation scheme is 256 QAM.

FIG. 86 is a diagram that illustrates an example of a constellation in a case where a modulation scheme is 1024 QAM.

FIG. 87 is a diagram that illustrates an example of coordinates of a signal point of a UC in a case where a modulation scheme is QPSK.

FIG. 88 is a diagram that illustrates an example of coordinates of a signal point of a 2D NUC in a case where a modulation scheme is 16 QAM.

FIG. 89 is a diagram that illustrates an example of coordinates of a signal point of a 2D NUC in a case where a modulation scheme is 64 QAM.

FIG. 90 is a diagram that illustrates an example of coordinates of a signal point of a 2D NUC in a case where a modulation scheme is 256 QAM.

FIG. 91 is a diagram that illustrates an example of coordinates of a signal point of a 2D NUC in a case where a modulation scheme is 256 QAM.

FIG. 92 is a diagram that illustrates an example of coordinates of a signal point of a 1D NUC in a case where a modulation scheme is 1024QAM.

FIG. 93 is a diagram that illustrates relations between a symbol y and a real part Re (z_(q)) and an imaginary part Im (z_(q)) of a complex number as coordinates of a signal point z_(q) of a 1D NUC corresponding to the symbol y.

FIG. 94 is a block diagram that illustrates a configuration example of a block interleaver 25.

FIG. 95 is a diagram that illustrates an example of the number C of columns of parts 1 and 2 and part column lengths R1 and R2 for each combination of a code length N and a modulation scheme.

FIG. 96 is a diagram that illustrates block interleave performed by a block interleaver 25.

FIG. 97 is a diagram that illustrates group-wise interleave performed by a group-wise interleaver 24.

FIG. 98 is a diagram that illustrates a first example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 99 is a diagram that illustrates a second example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 100 is a diagram that illustrates a third example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 101 is a diagram that illustrates a fourth example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 102 is a diagram that illustrates a fifth example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 103 is a diagram that illustrates a sixth example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 104 is a diagram that illustrates a seventh example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 105 is a diagram that illustrates an eighth example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 106 is a diagram that illustrates a ninth example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 107 is a diagram that illustrates a tenth example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 108 is a diagram that illustrates an 11th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 109 is a diagram that illustrates a 12th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 110 is a diagram that illustrates a 13th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 111 is a diagram that illustrates a 14th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 112 is a diagram that illustrates a 15th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 113 is a diagram that illustrates a 16th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 114 is a diagram that illustrates a 17th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 115 is a diagram that illustrates an 18th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 116 is a diagram that illustrates a 19th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 117 is a diagram that illustrates a 20th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 118 is a diagram that illustrates a 21st example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 119 is a diagram that illustrates a 22nd example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 120 is a diagram that illustrates a 23rd example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 121 is a diagram that illustrates a 24th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 122 is a diagram that illustrates a 25th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 123 is a diagram that illustrates a 26th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 124 is a diagram that illustrates a 27th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 125 is a diagram that illustrates a 28th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 126 is a diagram that illustrates a 29th example of a GW pattern for an LDPC code having a code length N of 64 k bits.

FIG. 127 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 128 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 129 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 130 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 131 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 132 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 133 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 134 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 135 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 136 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 137 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 138 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 139 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 140 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 141 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 142 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 143 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 144 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 145 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 146 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 147 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 148 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 149 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 150 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 151 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 152 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 153 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 154 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 155 is a diagram that illustrates a simulation result of a simulation of measuring an error rate.

FIG. 156 is a block diagram that illustrates a configuration example of a receiving device 12.

FIG. 157 is a block diagram that illustrates a configuration example of a bit deinterleaver 165.

FIG. 158 is a flowchart that illustrates an example of a process performed by a demapper 164, a bit deinterleaver 165, and an LDPC decoder 166.

FIG. 159 is a diagram that illustrates an example of a parity check matrix of an LDPC code.

FIG. 160 is a diagram that illustrates an example of a matrix (a transformed parity check matrix) acquired by performing a row permutation and a column permutation for a parity check matrix.

FIG. 161 is a diagram that illustrates an example of a transformed parity check matrix divided in units of 5×5.

FIG. 162 is a block diagram that illustrates a configuration example of a decoding device collectively performing P node operations.

FIG. 163 is a block diagram that illustrates a configuration example of an LDPC decoder 166.

FIG. 164 is a block diagram that illustrates a configuration example of a block deinterleaver 54.

FIG. 165 is a block diagram that illustrates another configuration example of a bit deinterleaver 165.

FIG. 166 is a block diagram that illustrates a first configuration example of a reception system to which the receiving device 12 can be applied.

FIG. 167 is a block diagram that illustrates a second configuration example of a reception system to which the receiving device 12 can be applied.

FIG. 168 is a block diagram that illustrates a third configuration example of a reception system to which the receiving device 12 can be applied.

FIG. 169 is a block diagram that illustrates a configuration example a computer according to an embodiment of the present technology.

MODE FOR CARRYING OUT THE INVENTION

Hereinafter, exemplary embodiments of the present technology will be described. Before the description thereof, an LDPC code will be described.

<LDPC Code>

Note that the LDPC code is a linear code and, here, will be described to have two dimensions here, although the two dimensions are not necessary.

A major characteristic of the LDPC code is that a parity check matrix defining the LDPC code is sparse. Here, a sparse matrix is a matrix in which the number of “1”s as elements of the matrix is very small (a matrix of which most elements are 0's).

FIG. 1 is a diagram that illustrates a parity check matrix H of an LDPC code.

In the parity check matrix H illustrated in FIG. 1, a weight (column weight) (the number of “1”s) of each column is “3” and a weight of each row (row weight) is “6”.

In coding using the LDPC code (LDPC coding), for example, a generation matrix G is generated on the basis of the parity check matrix H, and a code word (LDPC code) is generated by multiplexing information bits of two dimensions by the generation matrix G.

More specifically, a coding device that performs the LDPC coding, first, calculates the generation matrix G satisfying GH^(T)=0 for a transposed matrix H^(T) of the parity check matrix H. Here, in a case where the generation matrix G is a K×N matrix, the coding device generates a code word c (=uG) configured by N bits by multiplying the generation matrix G by a bit string (vector u) of information bits configured by K bits. The code word (LDPC code) that is generated by the coding device is received at a reception side through a predetermined communication line.

The LDPC code can be decoded by using a message passing algorithm, which is an algorithm proposed by Gallager by calling it as probabilistic decoding, using belief propagation on a so-called a Tanner graph formed by a variable node (also referred to as a message node) and a check node. Hereinafter, the variable node and the check node will be simply referred to as nodes as is appropriate.

FIG. 2 is a flowchart that illustrates a decoding sequence of an LDPC code.

Note that, hereinafter, a real value (a received LLR) that is acquired by representing the likelihood of “0” of a value of an i-th code bit of the LDPC code (one code word) received by the reception side by using a log likelihood ratio will be appropriately referred to as a reception value u_(0i). In addition, a message output from the check node will be referred to as u_(j), and a message output from the variable node will be referred to as v_(i).

First, in decoding the LDPC code, as illustrated in FIG. 2, in step S11, the LDPC code is received, the message (check node message) u_(j) is initialized to “0”, and a variable k taking an integer as a counter of repetition processes is initialized to “0”, and the process proceeds to step S12. In step S12, the message (variable node message) v_(i) is acquired by performing an operation (variable node operation) represented by Equation (1) on the basis of the reception value u_(0i) acquired by receiving the LDPC code, and the message u_(j) is acquired by performing an operation (check node operation) represented by Equation (2) on the basis of the message v_(i).

$\begin{matrix} \left\lbrack {{Mathematical}\mspace{14mu}{Formula}\mspace{14mu} 1} \right\rbrack & \; \\ {v_{i} = {u_{0i} + {\sum\limits_{j = 1}^{d_{v} - 1}\; u_{j}}}} & (1) \\ \left\lbrack {{Mathematical}\mspace{14mu}{Formula}\mspace{14mu} 2} \right\rbrack & \; \\ {{\tanh\left( \frac{u_{j}}{2} \right)} = {\prod\limits_{i = 1}^{d_{c} - 1}\;{\tanh\left( \frac{v_{i}}{2} \right)}}} & (2) \end{matrix}$

Here, d_(v) and d_(c) represented in Equations (1) and (2) respectively are parameters, which can be arbitrarily selected, representing the number of “1”s in the vertical direction (column) and the horizontal direction (row) of the parity check matrix H. For example, in case of an LDPC code ((3, 6) LDPC code) for the parity check matrix H having a column weight of 3 and a row weight of 6 as illustrated in FIG. 1, d_(v)=3 and d_(c)=6.

Note that, in the variable node operation represented in Equation (1) and the check node operation represented in Equation (2), since a message input from a branch (edge) (a line joining the variable node and the check node) from which a message is output is not a target for the operation, the range of the operation is 1 to d_(v)−1 or 1 to d_(c)−1. Actually, the check node operation represented by Equation (2) is performed by generating a table of a function R (v₁, v₂) represented by Equation (3) defined by one output for two inputs v₁ and v₂ in advance and continuously (recursively) using the table as represented by Equation (4). [Mathematical Formula 3] x=2 tan h ⁻¹{tan h(v ₁/2)tan h(v ₂/2)}=R(v ₁ ,v ₂)  (3) [Mathematical Formula 4] u _(j) =R(v ₁ ,R(v ₂ ,R(v ₃ , . . . R(v _(d) _(c) ⁻² ,v _(d) _(c) ⁻¹))))  (4)

In step S12, additionally, the variable k is incremented by “1”, and the process proceeds to step S13. In step S13, it is determined whether or not the variable k is larger than a predetermined repetition number C of times of decoding. In step S13, in a case where the variable k is determined not to be larger than the predetermined repetition number C of times, the process is returned to step S12, and thereafter, a similar process is repeated.

On the other hand, in a case where the variable k is determined to be larger than the predetermined repetition number C of times in step S13, the process proceeds to step S14, and, by performing an operation represented in Equation (5), a message v_(i) that is a final decoding result to be output is acquired and output, and the process of decoding the LDPC code ends.

[Mathematical  Formula  5] $\begin{matrix} {v_{i} = {u_{0i} + {\sum\limits_{j = 1}^{d_{v}}\; u_{j}}}} & (5) \end{matrix}$

Here, the operation represented in Equation (5), differently from the variable node operation represented in Equation (1), is performed using messages u_(j) from all the branches connected to the variable node.

FIG. 3 is a diagram that illustrates an example of a parity check matrix H of a (3, 6) LDPC code (a coding rate of 1/2 and a code length of 12).

In the parity check matrix H illustrated in FIG. 3, similarly to that illustrated in FIG. 1, a column weight is configured to be 3, and a row weight is configured to be 6.

FIG. 4 is a diagram that illustrates a Tanner graph of the parity check matrix H illustrated in FIG. 3.

Here, in FIG. 4, each check node is denoted by a plus sign “+”, and each variable node is denoted by an equal sign “=”. Here, check nodes and variable nodes respectively correspond to rows and columns of the parity check matrix H. A connected line between a check node and a variable node represents a branch (edge) and corresponds to “1” as an element of the parity check matrix.

In other words, in a case where an element of the j-th row and the i-th column of the parity check matrix is “1”, in FIG. 4, an i-th variable node (a node of “=”) from the top and a j-th check node (a node of “+”) from the top are connected together using a branch. The branch represents that a code bit corresponding to the variable node has a constraint condition corresponding to the check node.

In a sum product algorithm that is a method of decoding the LDPC code, a variable node operation and a check node operation are repeatedly performed.

FIG. 5 is a diagram that illustrates a variable node operation performed at a variable node.

At the variable node, a message v_(i) corresponding to a branch to be calculated is acquired using the variable node operation represented in Equation (1) using messages u₁ and u₂ from the remaining branches connected to the variable node and a reception value u_(0i). Messages corresponding to other branches are similarly acquired.

FIG. 6 is a diagram that illustrates a check node operation performed at a check node.

Here, the check node operation represented in Equation (2) can be rewritten into Equation (6) by using a relation of “a×b=exp{ln(|a|)+ln(|b|)}×sign(a)×sign(b)”. Here, sign(x) is 1 at the time of x≥0 and is −1 at the time of x<0.

[Mathematical  Formula  6] $\begin{matrix} \begin{matrix} {u_{j} =} & {2{\tanh^{- 1}\left( {\prod\limits_{i = 1}^{d_{c} - 1}\;{\tanh\left( \frac{v_{i}}{2} \right)}} \right)}} \\ {=} & {2{\tanh^{- 1}\left\lbrack {\exp\left\{ {\sum\limits_{i = 1}^{d_{c} - 1}\;{\ln\left( {{\tanh\left( \frac{v_{i}}{2} \right)}} \right)}} \right\} \times} \right.}} \\  & \left. {\prod\limits_{i = 1}^{d_{c} - 1}\;{{sign}\left( {\tanh\left( \frac{v_{i}}{2} \right)} \right)}} \right\rbrack \\ {=} & {2{\tanh^{- 1}\left\lbrack {\exp\left\{ {- \left( {\sum\limits_{i = 1}^{d_{c} - 1}\;{- {\ln\left( {\tanh\left( \frac{v_{i}}{2} \right)} \right)}}} \right)} \right\}} \right\rbrack} \times {\prod\limits_{i = 1}^{d_{c} - 1}\;{{sign}\left( v_{i} \right)}}} \end{matrix} & (6) \end{matrix}$

In case of x≥0, when a function ϕ(x) is defined using an equation ϕ(x)=ln(tan h(x/2)), an equation ϕ⁻¹(x)=2 tan h⁻¹(e^(−x)) is satisfied, and accordingly, Equation (6) can be transformed into Equation (7).

[Mathematical  Formula  7] $\begin{matrix} {u_{j} = {{\phi^{- 1}\left( {\sum\limits_{i = 1}^{d_{c} - 1}\;{\phi\left( {v_{i}} \right)}} \right)} \times {\prod\limits_{i = 1}^{d_{c} - 1}\;{{sign}\left( v_{i} \right)}}}} & (7) \end{matrix}$

At a check node, the check node operation represented in Equation (2) is performed according to Equation (7).

In other words, at a check node, as illustrated in FIG. 6, a message u_(j) corresponding to a branch to be calculated is acquired by performing the check node operation represented in Equation (7) using messages v₁, v₂, v₃, v₄, and v₅ from the remaining branches connected to the check node. Messages corresponding to the other branches are similarly acquired.

Note that the function ϕ(x) represented in Equation (7) can be represented using an equation ϕ(x)=ln((e^(x)+1)/(e^(x)−1)). Thus, in case of x>0, ϕ(x)=ϕ⁻¹ (x). In order to mount the functions ϕ(x) and ϕ⁻¹(x) to hardware, there are cases where the functions are mounted using a look up table (LUT). In such cases, both the functions use a same LUT.

<Configuration Example of Transmission System According to Present Technology>

FIG. 7 is a diagram that illustrates a configuration example of a transmission system (here, a system represents logical aggregation of a plurality of devices regardless of whether or not the devices of configurations are arranged inside a same casing) according to an embodiment of the present technology.

As illustrated in FIG. 7, the transmission system is configured by a transmitting device 11 and a receiving device 12.

The transmitting device 11, for example, transmits (broadcasts) (sends) a program of television broadcasting or the like. In other words, the transmitting device 11, for example, codes target data that is a transmission target such as image data, audio data, and the like as a program into an LDPC code and transmits the LDPC code through a communication line 13 such as a satellite link, a terrestrial wave, or a cable (wire circuit).

The receiving device 12 receives the LDPC code transmitted from the transmitting device 11 through the communication line 13, decodes the received LDPC code into target data, and outputs the target data.

Here, it is known that the LDPC code used by the transmission system illustrated in FIG. 7 shows a very high capability in an additive white Gaussian noise (AWGN) communication line.

Meanwhile, there are cases where a burst error or an erasure occurs in the communication line 13. For example, particularly, in a case where the communication line 13 is a terrestrial wave, in an orthogonal frequency division multiplexing (OFDM) system, in a multi-path environment in which a desired to undesired ratio (D/U) is 0 dB (the power of undesired=echo is the same as the power of desired=main path), the power of a specific symbol becomes zero in accordance with a delay of the echo (a path other than the main path) (erasure).

In addition, also in a flutter (a communication line, to which an echo of a Doppler frequency is added, having a delay of zero), in a case where the D/U is 0 dB, there are cases where the power of all the symbols of the OFDM at specific time becomes zero in accordance with a Doppler frequency (erasure).

In addition, there are cases where a burst error occurs according to the status of a wiring from a receiving unit (not illustrated in the drawing) such as an antenna receiving a signal from the transmitting device 11 to the receiving device 12 on the receiving device 12 side or the instability of the power supply of the receiving device 12.

Meanwhile, in decoding the LDPC code, at a variable node corresponding to a column of the parity check matrix H or furthermore, a code bit of the LDPC code, as illustrated in FIG. 5, since the variable node operation represented in Equation (1) accompanying the addition of code bits (the reception value u_(0i) thereof) of the LDPC code is performed, in a case where an error occurs in the code bits used for the variable node operation, the accuracy of an acquired message is decreased.

Then, in decoding the LDPC code, at a check node, since the check node operation represented in Equation (7) is performed using messages acquired at variable nodes connected to the check node, in a case where the number of check nodes for which errors (including erasures) simultaneously occur in a plurality of variable nodes (code bits of the LDPC code corresponding thereto) connected to each of the check nodes increases, the decoding performance is degraded.

In other words, for example, a check node, in a case where erasures simultaneously occur in two or more variable nodes connected to the check node, returns a message in which a probability of the value being “0” and a probability of the value being “1” are equal to all the variable nodes. In this case, the check node returning the message of the equal probability does not contribute to one decoding process (one set of the variable node operation and the check node operation) As a result, a large number of times of repetition of the decoding process are necessary, the decoding performance is degraded, and the power consumption of the receiving device 12 decoding the LDPC code is increased.

Thus, the transmission system illustrated in FIG. 7 can improve the resistance to a burst error or an erasure while maintaining the performance in the AWGN communication line (AWGN channel).

<Configuration Example of Transmitting Device 11>

FIG. 8 is a block diagram that illustrates a configuration example of the transmitting device 11 illustrated in FIG. 7.

In the transmitting device 11, one or more input streams are supplied to a mode adaptation/multiplexer 111 as target data.

The mode adaptation/multiplexer 111 performs mode selection and a process of multiplexing one or more input streams supplied thereto or the like as is necessary and supplies data acquired as a result thereof to a padder 112.

The padder 112 performs necessary zero filling (insertion of Null) for the data supplied from the mode adaptation/multiplexer 111 and supplies data acquired as a result thereof to a BB scrambler 113.

The BB scrambler 113 performs base-band scrambling (BB scrambling) for the data supplied from the padder 112 and supplies data acquired as a result thereof to a BCH encoder 114.

The BCH encoder 114 performs BCH coding of the data supplied from the BB scrambler 113 and supplies data acquired as a result thereof to an LDPC encoder 115 as LDPC target data that is a target for LDPC coding.

The LDPC encoder 115 performs LDPC coding according to a parity check matrix of which a parity matrix, which is a part corresponding to a parity bit of the LDPC code, has a dual diagonal structure or the like for the LDPC target data supplied from the BCH encoder 114 and outputs an LDPC code having the LDPC target data as information bits.

In other words, the LDPC encoder 115 performs LDPC coding, for example, for coding the LDPC target data into an LDPC code defined in a predetermined standard such as DVB-S.2, the DVB-T.2, the DVB-C.2, or the like, an LDPC code to be employed (corresponding to the check parity matrix) in ATSC 3.0, or the like and outputs the LDPC code acquired as a result thereof.

Here, the LDPC code defined in the standard of the DVB-T.2 and the LDPC code to be employed in ATSC 3.0 are irregular repeat accumulate (IRA) codes, and a parity matrix of the parity check matrix of the LDPC code has a staircase structure. The parity matrix and the staircase structure will be described later. The IRA code, for example, is described in “Irregular Repeat-Accumulate Codes”, H. Jin, A. Khandekar, and R. J. McEliece, in Proceedings of 2nd International Symposium on Turbo codes and Related Topics, pp. 1-8, September 2000.

The LDPC code output by the LDPC encoder 115 is supplied to a bit interleaver 116.

The bit interleaver 116 performs bit interleave to be described later for the LDPC code supplied from the LDPC encoder 115 and supplies the LDPC code after the bit interleave to a mapper 117.

The mapper 117 performs quadrature modulation (multi-value modulation) by mapping an LDPC code supplied from the bit interleaver 116 into a signal point representing one symbol of the quadrature modulation in units (symbol units) of code bits of one or more bits of the LDPC code.

In other words, the mapper 117 maps the LDPC code supplied from the bit interleaver 116 into a signal point, which is set in the modulation scheme performing quadrature modulation of the LDPC code, on an IQ plane (IQ constellation) defined by an I axis representing an I component having the same phase as the carrier wave and a Q axis representing a Q component orthogonal to the carrier wave and performs quadrature modulation.

In a case where the number of signal points set in the modulation scheme of the quadrature modulation performed by the mapper 117 is 2^(m), by using code bits of m bits of the LDPC code as a symbol (one symbol), in the mapper 117, the LDPC code supplied from the bit interleaver 116 is mapped into a signal point representing a symbol in units of symbols among the 2^(m) signal points.

Here, examples of the modulation scheme of the quadrature modulation performed by the mapper 117 include a modulation scheme defined in a standard such as DVB-T.2, a modulation scheme to be employed in ATSC 3.0, and other modulation schemes, in other words, includes Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), 8 Phase-Shift Keying (PSK), 16 Amplitude Phase-Shift Keying (APSK), 32 APSK, 16 Quadrature Amplitude Modulation (QAM), 16 QAM, 64 QAM, 256 QAM, 1024 QAM, 4096QAM, and 4 Pulse Amplitude Modulation (PAM). A modulation scheme by which the quadrature modulation is performed in the mapper 117 is set in advance, for example, according to an operation performed by an operator of the transmitting device 11.

The data (a mapping result acquired by mapping a symbol into a signal point) acquired by the process performed by the mapper 117 is supplied to a time interleaver 118.

The time interleaver 118 performs time interleave (interleave in the time direction) in units of symbols for the data supplied from the mapper 117 and supplies data acquired as a result thereof to a single input single output/multiple input single output encoder (SISO/MISO encoder) 119.

The SISO/MISO encoder 119 performs space-time coding for the data supplied from the time interleaver 118 and supplies the coded data to the frequency interleaver 120.

The frequency interleaver 120 performs frequency interleave (interleave in the frequency direction) in units of symbols for the data supplied from the SISO/MISO encoder 119 and supplies resultant data to a frame builder and resource allocation unit 131.

On the other hand, for example, control data (signalling) used for transfer control such as BB signaling (Base Band Signalling) (BB Header) is supplied to the BCH encoder 121.

The BCH encoder 121, similarly to the BCH encoder 114, performs the BCH coding for control data supplied thereto and supplies data acquired as a result thereof to an LDPC encoder 122.

The LDPC encoder 122, similarly to the LDPC encoder 115, performs LDPC coding of data supplied from the BCH encoder 121 as LDPC target data and supplies an LDPC code acquired as a result thereof to a mapper 123.

The mapper 123, similarly to the mapper 117, performs quadrature modulation by mapping an LDPC code supplied from the LDPC encoder 122 into a signal point representing one symbol of the quadrature modulation in units (symbol units) of code bits of one or more bits of the LDPC code and supplies data acquired as a result thereof to a frequency interleaver 124.

The frequency interleaver 124, similarly to the frequency interleaver 120, performs frequency interleave of data supplied from the mapper 123 in units of symbols and supplies resultant data to a frame builder/resource allocation unit 131.

The frame builder/resource allocation unit 131 inserts symbols of pilots into necessary positions of the data (symbols) supplied from the frequency interleavers 120 and 124, configures a frame (for example, a physical layer (PL) frame, a T2 frame, a C2 frame, or the like) configured by a predetermined number of symbols on the basis of resultant data (symbol) thereof, and supplies the configured frame to the OFDM generating unit (OFDM generation) 132.

The OFDM generating unit 132 generates an OFDM signal corresponding to the frame from the frame supplied from the frame builder/resource allocation unit 131 and transmits the OFDM signal through the communication line 13 (FIG. 7).

Note that the transmitting device 11, for example, may be configured without arranging some of the blocks illustrated in FIG. 8 such as the time interleaver 118, the SISO/MISO encoder 119, the frequency interleaver 120 and, the frequency interleaver 124.

<Configuration Example of Bit Interleaver 116>

FIG. 9 is a block diagram that illustrates a configuration example of the bit interleaver 116 illustrated in FIG. 8.

The bit interleaver 116 has a function of interleaving data and includes a parity interleaver 23, a group-wise interleaver 24, and a block interleaver 25.

The parity interleaver 23 performs parity interleave of interleaving the parity bits of the LDPC code supplied from the LDPC encoder 115 into positions of other parity bits and supplies the LDPC code after the parity interleave to the group-wise interleaver 24.

The group-wise interleaver 24 performs group-wise interleave for the LDPC code supplied from the parity interleaver 23 and supplies the LDPC code after the group-wise interleave to the block interleaver 25.

Here, in the group-wise interleave, an LDPC code supplied from the parity interleaver 23 is interleaved in units of bit groups by using 360 bits of one segment as a bit group that is acquired by dividing an LDPC code corresponding to one code from the start thereof in units of 360 bits that are the same as a unit size P to be described later.

In a case where the group-wise interleave is performed, the error rate can be improved to be better than that in a case where the group-wise interleave is not performed, and as a result, excellent communication quality can be secured in data transmission.

The block interleaver 25 symbolizes an LDPC code, for example, corresponding to one code into symbols of m bits as a unit for mapping by performing block interleave for demultiplexing the LDPC code supplied from the group-wise interleaver 24 and supplies the symbols to the mapper 117 (FIG. 8).

Here, in the block interleave, for example, an LDPC code corresponding to one code is converted into an m-bit symbol as the LDPC code supplied from the group-wise interleaver 24 is written in the column direction and is read in the row direction for a storage area in which columns as storage areas each storing a predetermined number of bits in the column (vertical) direction of the same number as the number m of bits of the symbol are aligned in the row (horizontal) direction.

<Parity Check Matrix H of LDPC Code>

FIG. 10 is a diagram that illustrates an example of the parity check matrix H used for LDPC coding by the LDPC encoder 115 illustrated in FIG. 8.

The parity check matrix H has a Low-Density Generation Matrix (LDGM) structure and can be represented by an equation H=[H_(A)|H_(T)] (a matrix having elements of an information matrix H_(A) as its left elements and having elements of a parity matrix H_(T) as its right elements) using the information matrix H_(A) Of a part corresponding to information bits among the code bits of the LDPC code and the parity matrix H_(T) corresponding to the parity bits thereof.

Here, among the code bits of the LDPC code (one code word) of one code, the bit number of information bits and the number bits of parity bits will be respectively referred to as an information length K and a parity length M, and the bit number of the code bits of one (one code word) LDPC code will be referred to as a code length N (=K+M).

The information length K and the parity length M of the LDPC code having a certain code length N are determined by a coding rate. The parity check matrix H is a matrix in which rows×columns are M×N (a matrix of M rows and N columns). The information matrix H_(A) is a matrix of M×K, and the parity matrix H_(T) is a matrix of M×M.

FIG. 11 is a diagram that illustrates an example of the parity matrix H_(T) of the parity check matrix H used for LDPC coding by the LDPC encoder 115 illustrated in FIG. 8.

The parity matrix H_(T) of the parity check matrix H used by the LDPC encoder 115 for LDPC coding, for example, is similar to a parity matrix H_(T) of a parity check matrix H of an LDPC code defined in the standard of DVB-T.2 or the like.

The parity matrix H_(T) of the parity check matrix H of the LDPC code that is defined in the standard of DVB-T.2 or the like, as illustrated in FIG. 11, is a matrix (lower bidiagonal matrix) having a staircase structure in which elements of “1” are aligned in a staircase pattern. The row weight of the parity matrix H_(T) is 1 in a first row and is 2 in all the remaining rows. In addition, the column weight is 1 for the last one column and is 2 for all the remaining columns.

As described above, the LDPC code of the parity check matrix H of which the parity matrix H_(T) has the staircase structure can be easily generated using the parity check matrix H.

In other words, the LDPC code (one code word) will be represented by a row vector c, and a column vector acquired by transposing the row vector will be represented by c^(T). In addition, an information-bit part of the row vector c that is the LDPC code will be represented by a row vector A, and a parity-bit part thereof will be represented by a row vector T.

In this case, the row vector c can be represented by an equation c=[A|T] (having elements of a column vector A as left elements and having elements of a row vector T as right elements) by using the column vector A as information bits and the row vector T as parity bits.

In the parity check matrix H and the row vector c=[A|T] as the LDPC code need to satisfy an equation Hc^(T)=0. The row vector T as the parity bits configuring the row vector c=[A|T] satisfying the equation Hc^(T)=0 can be sequentially (orderly) acquired by setting elements of each row to “0” sequentially from elements of the first row of the column vector Hc^(T) in the equation Hc^(T)=0 in a case where the parity matrix H_(T) of the parity check matrix H=[H_(A)|H_(T)] has the staircase structure illustrated in FIG. 11.

FIG. 12 is a diagram that illustrates a parity check matrix H of an LDPC code defined in the standard of DVB-T.2 or the like.

For KX columns from a first column of the parity check matrix H of the LDPC code defined in the standard of DVB-T.2 or the like, the column weight is set to X, for the following K3 columns, the column weight is set to “3”, for the following (M−1) columns, the column weight is set to “2”, and, for the last one column, the column weight is set to “1”.

Here, KX+K3+M−1+1 is equal to the code length N.

FIG. 13 is a diagram that illustrates the numbers KX, K3, and M of columns and a column weight X for each coding rate r of the LDPC code defined in the standard of DVB-T.2.

In the standard of the DVB-T.2 or the like, LDPC codes, which have a code length N, of 64800 bits and 16200 bits are defined.

For the LDPC code of which the code length N is 64800 bits, 11 coding rates (nominal rates) of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, and 9/10 are defined. In addition, for the LDPC code of which the code length N is 16200 bits, 10 coding rates of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, and 8/9 are defined.

Here, the code length N of the 64800 bits may be also referred to as 64 kbits, and the code length N of the 16200 bits may be also referred to as 16 kbits.

For the LDPC code, an error rate tends to be lower in a code bit corresponding to a column of which a column weight of the parity check matrix H is larger.

In the parity check matrix H, which is illustrated in FIGS. 12 and 13, defined in the standard of the DVB-T.2 or the like, a column weight of a column tends to increase as the column is disposed on a further head side (left side). Accordingly, for the LDPC code corresponding to the parity check matrix H, a code bit disposed on a further head side tends to be more resistant against an error (have resistance against an error), and, a last code bit tends to be less resistant against an error.

<Parity Interleave>

Next, the parity interleave performed by the parity interleaver 23 illustrated in FIG. 9 will be described with reference to FIGS. 14 to 16.

FIG. 14 is a diagram that illustrates an example of a Tanner graph (a part thereof) of a parity check matrix of an LDPC code.

As illustrated in FIG. 14, when errors simultaneously occur such as erasures in a plurality of variable nodes such as two variable nodes (code bits corresponding thereto) connected to a check node, the check node returns a message in which a probability of the value being “0” and a probability of the value being “1” are equal to all the variable nodes connected to the check node. For this reason, when erasures or the like simultaneously occur in the plurality of variable nodes connected to same check node, the decoding performance is degraded.

Meanwhile, the LDPC code output by the LDPC encoder 115 illustrated in FIG. 8, for example, is an IRA code, similarly to the LDPC code defined in the standard of the DVB-T.2 or the like, and the parity matrix H_(T) of the parity check matrix H, as illustrated in FIG. 11, has a staircase structure.

FIG. 15 is a diagram that illustrates an example of a parity matrix H_(T) having a staircase structure and a Tanner graph corresponding to the parity matrix H_(T), as illustrated in FIG. 11.

A of FIG. 15 illustrates an example of a parity matrix H_(T) having a staircase structure, and B of FIG. 15 illustrates a Tanner graph corresponding to the parity matrix H_(T) illustrated in A of FIG. 15.

In the parity matrix H_(T) having a staircase structure, elements of “1” are adjacent to each other in each row (except for the first row). For this reason, in the Tanner graph of the parity matrix H_(T), two adjacent variable nodes corresponding to columns of two adjacent elements of which the values of the parity matrix H_(T) are “1”s are connected to a same check node.

Accordingly, when errors simultaneously occur in parity bits corresponding to the two adjacent variable nodes described above in accordance with burst errors, erasures, or the like, a check node connected to the two variable nodes (variable nodes acquiring messages using parity bits) corresponding to the two parity bits in which the errors occur returns a message in which a probability of the value being “0” and a probability of the value being “1” are equal to the variable nodes connected to the check node, and accordingly, the decoding performance is degraded. Then, when a burst length (the bit number of parity bits in which errors continuously occur) is large, the number of check nodes each returning a message of the equal probability increases, and the decoding performance is further degraded.

Accordingly, in order to prevent the degradation of the decoding performance described above, the parity interleaver 23 (FIG. 9) performs parity interleave in which parity bits of the LDPC code supplied from the LDPC encoder 115 are interleaved to positions of the other parity bits.

FIG. 16 is a diagram that illustrates a parity matrix H_(T) of a parity check matrix H corresponding to an LDPC code after the parity interleave performed by the parity interleaver 23 illustrated in FIG. 9.

Here, the information matrix H_(A) of the parity check matrix H corresponding to the LDPC code output by the LDPC encoder 115, similarly to the information matrix of the parity check matrix H corresponding to the LDPC code defined in the standard of DVB-T.2 or the like, has a cyclic structure.

The cyclic structure represents a structure in which a certain column coincides with a column acquired by cyclically shifting another column and, for example, also includes a structure in which, for every P columns, the position of “1” in each column of the P columns is a position acquired by cyclically shifting a first column of the P columns in a column direction by a predetermined value such as a value proportional to a value q acquired by dividing the parity length M. Hereinafter, P columns in the cyclic structure will be referred to as a unit size.

As LDPC codes defined in the standard of DVB-T.2 or the like, as described with reference to FIGS. 12 and 13, there are two types of LDPC codes of which the code lengths N are 64800 bits and 16200 bits, and, for each of those two types of LDPC codes, the unit size P is defined as 360 that is one of divisors of the parity length M excluding 1 and M.

The parity length M has a value other than prime numbers that is represented by an equation M=q×P=q×360 using a value q different according to the coding rate. Therefore, similarly to the unit size P, the value q is another one of the divisors of the parity length M other than 1 and M and is acquired by dividing the parity length M by the unit size P (the product of P and q that are the divisors of the parity length M is the parity length M).

As described above, when the information length is K, an integer equal to or greater than 0 and smaller than P is set to x, and an integer equal to or greater than 0 and smaller than q is set to y, the parity interleaver 23 interleaves a (K+qx+y+1)-th code bit of code bits of an LDPC code configured by N bits at the position of the (K+Py+x+1)-th code bit as parity interleave.

Both the (K+qx+y+1)-th code bit and the (K+Py+x+1)-th code bit are code bits after the (K+1)-th bit and thus are parity bits. Therefore, according to the parity interleave, the positions of the parity bits of the LDPC code are moved.

According to the parity interleave, variable nodes (parity bits corresponding thereto) connected to a same check node are separated by the unit size P, that is, 360 bits in this case. Therefore, in a case where the burst length is less than 360 bits, a situation in which errors simultaneously occur at a plurality of variable nodes connected to the same check node can be avoided, and as a result thereof, the resistance against a burst error can be improved.

Note that the LDPC code after the parity interleave for interleaving the (K+qx+y+1)-th code bit into the position of the (K+Py+x+1)-th code bit coincides with an LDPC code of a parity check matrix (hereinafter, referred to as a transformed parity check matrix) acquired by performing column permutation for replacing a (K+qx+y+1)-th column of the original parity check matrix H with a (K+Py+x+1)-th column.

In addition, in the parity matrix of the transformed parity check matrix, as illustrated in FIG. 16, a pseudo cyclic structure configured in units of P columns (in the case illustrated in FIG. 16, 360 columns) appears.

Here, the pseudo cyclic structure is a structure in which a portion acquired by excluding a part has a cyclic structure.

In the transformed parity check matrix acquired by performing the column permutation corresponding to the parity interleave for the parity check matrix of the LDPC code defined in the standard of DVB-T.2 or the like, in a part of 360 rows×360 columns (a shift matrix to be described later) disposed in an upper right corner portion of the transformed parity check matrix, one of the elements of “1” is lacking (instead, the element is element of “0”). From that point, the transformed parity check matrix has not a (complete) cyclic structure but a so-called pseudo cyclic structure.

The transformed parity check matrix for the parity check matrix of the LDPC code output by the LDPC encoder 115, for example, similarly to the transformed parity check matrix for the parity check matrix of the LDPC code defined in the standard of DVB-T.2 or the like, has a pseudo cyclic structure.

Note that the transformed parity check matrix illustrated in FIG. 16 is a matrix acquired by performing permutation of rows for configuring the transformed parity check matrix to be a constituent matrix to be described later for the original parity check matrix H in addition to the column permutation corresponding to the parity interleave.

FIG. 17 is a flowchart that illustrates a process performed by the LDPC encoder 115, the bit interleaver 116, and the mapper 117 illustrated in FIG. 8.

The LDPC encoder 115 waits for the supply of the LDPC target data from the BCH encoder 114. Then, in step S101, the LDPC encoder 115 codes LDPC target data into an LDPC code and supplies the LDPC code to the bit interleaver 116, and the process proceeds to step S102.

In step S102, the bit interleaver 116 performs bit interleave for the LDPC code supplied from the LDPC encoder 115 as a target and supplies a symbol acquired by the bit interleave to the mapper 117, and the process proceeds to step S103.

In other words, in step S102, in the bit interleaver 116 (FIG. 9), the parity interleaver 23 performs parity interleave for the LDPC code supplied from the LDPC encoder 115 as a target and supplies the LDPC code after the parity interleave to the group-wise interleaver 24.

The group-wise interleaver 24 performs the group-wise interleave for the LDPC code supplied from the parity interleaver 23 as a target and supplies resultant LDPC code to the block interleaver 25.

The block interleaver 25 performs the block interleave for the LDPC code after the group-wise interleave performed by the group-wise interleaver 24 as a target and supplies a symbol of m bits acquired as a result thereof to the mapper 117.

In step S103, the mapper 117 performs quadrature modulation by mapping the symbol supplied from the block interleaver 25 to one of 2^(m) signal points determined in the modulation scheme of the quadrature modulation performed by the mapper 117 and supplies data acquired as a result thereof to the time interleaver 118.

As described above, by performing the parity interleave and the group-wise interleave, an error rate in a case where a plurality of code bits of the LDPC code are transmitted as one symbol can be improved.

Here, in the case illustrated in FIG. 9, for the convenience of description, while the parity interleaver 23 that is a block performing the parity interleave and the group-wise interleaver 24 that is a block performing the group-wise interleave are separately configured, the parity interleaver 23 and the group-wise interleaver 24 may be integrally configured.

In other words, both the parity interleave and the group-wise interleave can be performed by writing and reading the code bits for the memory and can be represented by a matrix that converts an address (write address) into which code bits are written into an address (read address) from which code bits are read.

Accordingly, in a case where a matrix that is acquired by multiplying a matrix representing the parity interleave by a matrix representing the group-wise interleave is acquired, by converting code bits by using such matrixes, the parity interleave is performed, and a result of the group-wise interleave of the LDPC code after the parity interleave can be acquired.

In addition to the parity interleaver 23 and the group-wise interleaver 24, the block interleaver 25 can be integrally configured.

In other words, the block interleave performed by the block interleaver 25 also can be represented by using a matrix that converts a write address of the memory in which the LDPC code is stored into a read address.

Therefore, by acquiring a matrix that is acquired by multiplying the matrix representing the parity interleave by the matrix representing the group-wise interleave and the matrix representing the block interleave, the parity interleave, the group-wise interleave, and the block interleave can be performed together by using the matrix.

<Configuration Example of the LDPC Encoder 115>

FIG. 18 is a block diagram that illustrates a configuration example of the LDPC encoder 115 illustrated in FIG. 8.

Note that the LDPC encoder 122 illustrated in FIG. 8 is similarly configured.

As described with reference to FIGS. 12 and 13, in the standard of the DVB-T.2 or the like, the LDPC codes of two types of code lengths N including 64800 bits and 16200 bits are defined.

For the LDPC code having the code length N of 64800 bits, 11 coding rates of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 8/9, and 9/10 are defined. In addition, for the LDPC code having the code length N of 16200 bits, 10 coding rates of 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, and 8/9 are defined (FIGS. 12 and 13).

For example, the LDPC encoder 115 can perform coding (error correction coding) using the LDPC code of each coding rate having the code length N of 64800 bits or 16200 bits by using the parity check matrix H prepared for each code length N and each coding rate.

The LDPC encoder 115 includes a coding processing unit 601 and a storage unit 602.

The coding processing unit 601 is configured by: a coding rate setting unit 611, an initial value table reading unit 612; a parity check matrix generating unit 613; an information bit reading unit 614; a coding parity calculating unit 615; and a control unit 616. The coding processing unit 601 performs the LDPC coding of LDPC target data supplied to the LDPC encoder 115 and supplies an LDPC code acquired as a result thereof to the bit interleaver 116 (FIG. 8).

In other words, the coding rate setting unit 611, for example, sets the code length N and the coding rate of the LDPC code in accordance with operator's operation or the like.

The initial value table reading unit 612 reads a parity check matrix initial value table to be described later corresponding to the code length N and the coding rate set by the coding rate setting unit 611 from the storage unit 602.

The parity check matrix generating unit 613 generates a parity check matrix H by arranging elements of 1 of an information matrix H_(A) corresponding to an information length K (=code length N−parity length M) according to the code length N and the coding rate set by the coding rate setting unit 611 in the column direction at the period of 360 columns (unit size P) on the basis of the parity check matrix initial value table read by the initial value table reading unit 612 and stores the parity check matrix H in the storage unit 602.

The information bit reading unit 614 reads (extracts) information bits corresponding to the information length K from the LDPC target data supplied to the LDPC encoder 115.

The coding parity calculating unit 615 reads the parity check matrix H generated by the parity check matrix generating unit 613 from the storage unit 602 and generates a code word (LDPC code) by calculating parity bits for the information bits read by the information bit reading unit 614 by using the parity check matrix H on the basis of a predetermined equation.

The control unit 616 controls each block that configures the coding processing unit 601.

In the storage unit 602, a plurality of parity check matrix initial value tables corresponding to the plurality of coding rates, which are illustrated in FIGS. 12 and 13, for the code lengths N such as 64800 bits and 16200 bits are stored. In addition, the storage unit 602 temporarily stores data that is necessary for processing performed by the coding processing unit 601.

FIG. 19 is a flowchart that illustrates an example of the process performed by the LDPC encoder 115 illustrated in FIG. 18.

In step S201, the coding rate setting unit 611 determines (sets) the code length N and the coding rate r for performing the LDPC coding.

In step S202, the initial value table reading unit 612 reads a parity check matrix initial value table, which is set in advance, corresponding to the code length N and the coding rate r determined by the coding rate setting unit 611 from the storage unit 602.

In step S203, the parity check matrix generating unit 613 acquires (generates) the parity check matrix H of the LDPC code of the code length N and the coding rate r determined by the coding rate setting unit 611 by using the parity check matrix initial value table read from the storage unit 602 by the initial value table reading unit 612 and supplies the acquired parity check matrix H to the storage unit 602 so as to be stored therein.

In step S204, the information bit reading unit 614 reads the information bits of the information length K (=N×r) corresponding to the code length N and the coding rate r determined by the coding rate setting unit 611 from the LDPC target data supplied to the LDPC encoder 115, reads the parity check matrix H acquired by the parity check matrix generating unit 613 from the storage unit 602, and supplies the information bits and the parity check matrix to the coding parity calculating unit 615.

In step S205, the coding parity calculating unit 615 sequentially calculates parity bits of a code word c satisfying Equation (8) using the information bits and the parity check matrix H supplied from the information bit reading unit 614. Hc ^(T)=0  (8)

In Equation (8), c represents a row vector as a code word (LDPC code), and c^(T) represents transposition of the row vector c.

Here, as described above, when a portion of information bits of the row vector c as the LDPC code (one code word) is represented as a row vector A, and a portion of parity bits thereof is represented as a row vector T, the row vector c can be represented by Equation c=[A|T] using the row vector A as the information bits and the row vector T as the parity bits.

The parity check matrix H and the row vector c=[A|T] as an LDPC code need to satisfy an equation Hc^(T)=0. The row vector T as the parity bits configuring the row vector c=[A|T] satisfying the equation Hc^(T)=0 can be sequentially calculated by setting elements of each row to 0 sequentially from elements of a first row of the column vector Hc^(T) in the equation Hc^(T)=0 in a case where the parity matrix H_(T) of the parity check matrix H=[H_(A)|H_(T)] has the staircase structure illustrated in FIG. 11.

The coding parity calculating unit 615 acquires parity bits T for the information bits A supplied from the information bit reading unit 614 and outputs a codeword c=[A|T] represented by the information bits A and the parity bits T as a result of the LDPC coding of the information bits A.

Thereafter, in step S206, the control unit 616 determines whether or not the LDPC coding ends. In a case where the LDPC coding is determined not to end in step S206, in other words, in a case where there is still LDPC target data for which the LDPC coding is performed, the process is returned to step S201 (or step S204). Thereafter, the process of steps S201 (or step S204) to S206 is repeated.

On the other hand, in step S206, in a case where the LDPC coding is determined to end, in other words, for example, in a case where there is no LDPC target data for which the LDPC coding is performed, the LDPC encoder 115 ends the process.

As described above, the parity check matrix initial value table corresponding to each code length N and each coding rate r is prepared in advance, and the LDPC encoder 115 performs the LDPC coding of the predetermined code length N and the predetermined coding rate r by using the parity check matrix H generated from the parity check matrix initial value table corresponding to the predetermined code length N and the predetermined coding rate r.

<Example of the Parity Check Matrix Initial Value Table>

The parity check matrix initial value table is a table that represents positions of elements of “1” in of the information matrix H_(A) (FIG. 10) of the parity check matrix H corresponding to the information length K according to the code length N and the coding rate r of the LDPC code (LDPC code defined according to the parity check matrix H) for every 360 columns (unit size P) and is generated in advance for each parity check matrix H of each code length N and each coding rate r.

In other words, the parity check matrix initial value table represents at least positions of elements of “1” in the information matrix H_(A) for every 360 columns (unit size P).

In addition, as such parity check matrixes H, there are a parity check matrix in which the (whole) parity matrix H_(T) has a staircase structure defined in DVB-T.2 or the like and a parity check matrix in which a part of the parity matrix H_(T) has a staircase structure, and the remaining portion is a diagonal matrix (unit matrix) proposed by CRC/ETRI.

Hereinafter, a representation scheme of a parity check matrix initial value table representing the parity check matrix in which the parity matrix H_(T) has the staircase structure defined in DVB-T.2 or the like will be referred to as a DVB type, and a representation scheme of a parity check matrix initial value table representing the parity check matrix proposed by CRC/ETRI will be referred to as an ETRI type.

FIG. 20 is a diagram that illustrates an example of the parity check matrix initial value table of the DVB type.

In other words, FIG. 20 illustrates a parity check matrix initial value table for the parity check matrix H, which is defined in the standard of the DVB-T.2, having a code length N of 16200 bits and a coding rate (a coding rate in the notation of the DVB-T.2) r of 1/4.

The parity check matrix generating unit 613 (FIG. 18) acquires the parity check matrix H as below by using the parity check matrix initial value table of the DVB type.

FIG. 21 is a diagram that illustrates a method of calculating a parity check matrix H by using a parity check matrix initial value table of the DVB type.

In other words, FIG. 21 illustrates a parity check matrix initial value table for the parity check matrix H, which is defined in the standard of the DVB-T.2, having a code length N of 16200 bits and a coding rate r of 2/3.

The parity check matrix initial value table of the DVB type is the table that represents the positions of elements of “1” of the whole information matrix H_(A) corresponding to the information length K according to the code length N and the coding rate r of the LDPC code for every 360 columns (unit size P). In the i-th row thereof, row numbers (row numbers when a row number of a first row of the parity check matrix H is set to “0”) of elements of “1” of a (1+360×(i−1))-th column of the parity check matrix H are arranged corresponding to the number of column weights of the (1+360×(i−1))-th column.

Here, since the parity matrix H_(T) (FIG. 10) of the parity check matrix H of the DVB type that corresponds to the parity length M is set to the staircase structure illustrated in FIG. 15, the parity check matrix H can be acquired in a case where the information matrix H_(A) (FIG. 10) corresponding to the information length K can be acquired using the parity check matrix initial value table.

The number k+1 of the rows of the parity check matrix initial value table of the DVB type is different according to the information length K.

A relation of Equation (9) is satisfied between the information length K and the number k+1 of rows of the parity check matrix initial value table. K=(k+1)×360  (9)

Here, 360 represented in Equation (9) is the unit size P described with reference to FIG. 16.

In the parity check matrix initial value table illustrated in FIG. 21, 13 numerical values are arranged from the first row to the third row, and three numerical values are arranged from the fourth row to the (k+1)-th row (in FIG. 21, the 30th row).

Accordingly, the column weights of the parity check matrix H that are acquired from the parity check matrix initial value table illustrated in FIG. 21 are 13 from the first column to the (1+360×(3−1)−1)-th column and are 3 from the (1+360×(3−1))-th column to the K-th column.

The first row of the parity check matrix initial value table of FIG. 21 represents 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620, and 2622, which represents that elements of rows having row numbers of 0, 2084, 1613, 1548, 1286, 1460, 3196, 4297, 2481, 3369, 3451, 4620, and 2622 are “1”s (and the other elements are “0”) in the first column of the parity check matrix H.

In addition, the second row of the parity check matrix initial value table illustrated in FIG. 21 represents 1, 122, 1516, 3448, 2880, 1407, 1847, 3799, 3529, 373, 971, 4358, and 3108, which represents that elements of rows having row numbers of 1, 122, 1516, 3448, 2880, 1407, 1847, 3799, 3529, 373, 971, 4358, and 3108 are “1”s in the 361 (=1+360×(2−1))-th column of the parity check matrix H.

As described above, the parity check matrix initial value table represents positions of elements of “1” in the information matrix H_(A) Of the parity check matrix H for every 360 columns.

The columns other than the (1+360×(i−1))-th column of the parity check matrix H, in other words, the columns of the (2+360×(i−1))-th column to the (360×i)-th column are arranged by cyclically shifting elements of “1” of the (1+360×(i−1))-th column set in the parity check matrix initial value table periodically in a downward direction (downward direction of the columns) along the parity length M.

In other words, for example, the (2+360×(i−1))-th column is acquired by cyclically shifting the (1+360×(i−1))-th column in the downward direction by M/360 (=q), and the next (3+360×(i−1))-th column is acquired by cyclically shifting the (1+360×(i−1))-th column in the downward direction by 2×M/360 (=2×q) (acquired by cyclically shifting the (2+360×(i−1))-th column in the downward direction by M/360 (=q)).

When a numerical value of a j-th column (a j-th column from the left side) of an i-th row (an i-th row from the upper side) of the parity check matrix initial value table is represented as h_(i,j), and a row number of the j-th element of “1” of the w-th column of the parity check matrix H is represented as H_(w-j), the row number H_(w-j) of the element of “1” of the w-th column that is a column other than the (1+360×(i−1))-th column of the parity check matrix H can be calculated using Equation (10). H _(w-j)=mod{h _(i,j)+mod((w−1),P)×q,M)  (10)

Here, mod(x, y) represents a remainder that is acquired by dividing x by y.

In addition, P is the unit size described above and, in this embodiment is 360, for example, similarly to the standards of the DVB-S.2, the DVB-T.2, and the DVB-C.2. Furthermore, q is a value M/360 that is acquired by dividing the parity length M by the unit size P (=360).

The parity check matrix generating unit 613 (FIG. 18) specifies the row numbers of elements of “1” of the (1+360×(i−1))-th column of the parity check matrix H by using the parity check matrix initial value table.

In addition, the parity check matrix generating unit 613 (FIG. 18) calculates the row number H_(w-j) of the element of “1” of the w-th column that is a column other than the (1+360×(i−1))-th column of the parity check matrix H by using Equation (10) and generates a parity check matrix H in which the element of the row number acquired as above is set to “1”.

FIG. 22 is a diagram that illustrates the structure of the parity check matrix of the ETRI type.

The parity check matrix of the ETRI type is configured by an A matrix, a B matrix, a C matrix, a D matrix, and a Z matrix.

The A matrix is an upper left matrix of the parity check matrix that has g rows and K columns represented by a predetermined value g and the information length K of the LDPC code wherein K=code length N×coding rate r.

The B matrix is a matrix having the staircase structure, which is configured by g rows and g columns, adjacent to the right side of the A matrix.

The C matrix is a matrix, which is configured by (N−K−g) rows and (K+g) columns, adjacent to the lower side of the A matrix and the B matrix.

The D matrix is a unit matrix, which is configured by (N−K−g) rows and (N−K−g) columns, adjacent to the right of the C matrix.

The Z matrix is a zero matrix (zero matrix), which is configured by g rows and (N−K−g) columns, adjacent to the right side of the B matrix.

In the parity check matrix of the ETRI type configured by the A to D matrices and the Z matrix as above, the A matrix and a portion of the C matrix configure an information matrix, and the B matrix, the remaining portion of the C matrix, the D matrix, and the Z matrix configure a parity matrix.

Note that, since the B matrix is a matrix having the staircase structure, and the D matrix is a unit matrix, a portion (a portion of the B matrix) of the parity matrix of the parity check matrix of the ETRI type has a staircase structure, and the remaining portion (the portion of the D matrix) is a diagonal matrix (unit matrix).

Similarly to the information matrix of the parity check matrix of the DVB type, the A matrix and the C matrix have a cyclic structure for every 360 columns (the unit size P), and the parity check matrix initial value table of the ETRI type represents positions of elements of “1” of the A matrix and the C matrix for every 360 columns.

Here, as described above, since the A matrix and a portion of the C matrix configure the information matrix, it can be determined that the parity check matrix initial value table of the ETRI type representing positions of elements “1” of the A matrix and the C matrix for every 360 columns represents at least positions of elements “1” of the information matrix for every 360 columns.

FIG. 23 is a diagram that illustrates an example of a parity check matrix initial value table of the ETRI type.

In other words, FIG. 23 illustrates an example of a parity check matrix initial value table for a parity check matrix having a code length N of 50 bits and a coding rate r of 1/2.

The parity check matrix initial value table of the ETRI type is a table that represents positions of elements “1” of the A matrix and the C matrix for each unit size P, and, in an i-th row, row numbers (row numbers when a row number of a first row of the parity check matrix is 0) of elements “1” of a (1+P×(i−1))-th column of the parity check matrix that correspond to the number of column weights included in the (1+P×(i−1))-th column are arranged.

Note that, here, for the simplification of description, the unit size P, for example, is assumed to be set to 5.

In addition, for the parity check matrix of the ETRI type, as parameters, there are g=M₁, M₂, Q₁, and Q₂.

g=M₁ is a parameter used for determining the size of the B matrix and has a value that is a multiple of the unit size P. The performance of the LDPC code is changed by adjusting g=M₁, and g=M₁ is adjusted to a predetermined value when the parity check matrix is determined. Here, 15, which is three times the unit size P=5, is assumed to be employed as g=M₁.

M₂ has a value M−M₁ acquired by subtracting M₁ from the parity length M.

Here, since the information length K is N×r=50×1/2=25, and the parity length M is N−K=50−25=25, M₂ is M−M₁=25−15=10.

Q₁ is acquired using an equation Q₁=M₁/P and represents the number of shifts (the number of rows) of the cyclic shift in the A matrix.

In other words, in each column other than the (1+P×(i−1))-th column of the A matrix of the parity check matrix of the ETRI type, in other words, in each of a (2+P×(i−1))-th column to a (P×i)-th column, elements “1” of a (1+360×(i−1))-th column set in the parity check matrix initial value table are periodically cyclically shifted in a downward direction (a downward direction of the column) so as to be arranged, and Q₁ represents the number of shifts of the cyclic shift in the A matrix.

Q₂ is acquired using an equation Q₂=M₂/P and represents the number of shifts (the number of rows) of the cyclic shift in the C matrix.

In other words, in each column other than the (1+P×(i−1))-th column of the C matrix of the parity check matrix of the ETRI type, in other words, in each of a (2+P×(i−1))-th column to a (P×i)-th column, elements “1” of a (1+360×(i−1))-th column set in the parity check matrix initial value table are periodically cyclically shifted in the downward direction (the downward direction of the column) so as to be arranged, and Q₂ represents the number of shifts of the cyclic shift in the C matrix.

Here, Q₁ is M₁/P=15/5=3, and Q₂ is M₂/P=10/5=2.

In the parity check matrix initial value table illustrated in FIG. 23, 3 numerical values are arranged in 1st and 2nd rows, and one numerical value is arranged in 3rd to 5th rows, and according to such an arrangement of the numerical values, the column weight of the parity check matrix acquired from the parity check matrix initial value table illustrated in FIG. 23 is 3 in the 1st column to a (1+5×(2−1)−1)-th column and is 1 in a (1+5×(2−1))-th column to a 5th column.

In other words, 2, 6, and 18 are arranged in the 1st row of the parity check matrix initial value table illustrated in FIG. 23, which represents that elements of rows having row numbers of 2, 6, and 18 are “1” (and the other elements are “0”) in the 1st column of the parity check matrix.

Here, in this case, since the A matrix is a matrix having 15 rows and 25 columns (g rows and K columns), and the C matrix is a matrix having 10 rows and 40 columns ((N−K−g) rows and (K+g) columns), rows having the row numbers of 0 to 14 in the parity check matrix are rows of the A matrix, and rows having the row numbers of 15 to 24 in the parity check matrix are rows of the C matrix.

Thus, among the rows having the row numbers of 2, 6, and 18 (hereinafter represented as rows #2, #6, and #18), the rows #2 and #6 are the rows of the A matrix, and the row #18 is the row of the C matrix.

In the 2nd row of the parity check matrix initial value table illustrated in FIG. 23, 2, 10, and 19 are arranged, which represents that elements of the rows #2, #10, and #19 are “1”s in a 6 (=1+5×(2−1))-th column of the parity check matrix.

Here, in the 6 (=1+5×(2−1))-th column of the parity check matrix, among rows #2, #10, and #19, the rows #2 and #10 are the rows of the A matrix, and the row #19 is the row of the C matrix.

In the 3rd row of the parity check matrix initial value table illustrated in FIG. 23, 22 is arranged, which represents that an element of the row #22 is “1” in an 11 (=1+5×(3−1))-th column of the parity check matrix.

Here, in the 11 (=1+5×(3−1))-th column of the parity check matrix, the row #22 is the row of the C matrix.

Similarly, 19 arranged in the 4th row of the parity check matrix initial value table illustrated in FIG. 23 represents that an element of the row #19 is “1” in a 16 (=1+5×(4−1))-th column of the parity check matrix, and 15 arranged in the 5th row of the parity check matrix initial value table illustrated in FIG. 23 represents that an element of the row #15 is “1” in a 21(=1+5×(5−1))-st column of the parity check matrix.

As described above, the parity check matrix initial value table represents the positions of elements “1” of the A matrix and the C matrix of the parity check matrix for each unit size P=5 columns.

In each column other than a (1+5×(i−1))-th column of the A matrix and the C matrix of the parity check matrix, in other words, in each of a (2+5×(i−1))-th column to a (5×i)-th column, the elements “1” of the (1+5×(i−1))-th column set in the parity check matrix initial value table are periodically cyclically shifted in the downward direction (the downward direction of the column) so as to be arranged according to the parameters Q₁ and Q₂.

In other words, for example, in the (2+5×(i−1))-th column of the A matrix, the (1+5×(i−1))-th column is cyclically shifted in the downward direction by Q₁ (=3), and, in the next (3+5×(i−1))-th column, the (1+5×(i−1))-th column is cyclically shifted in the downward direction by 2×Q₁ (=2×3) (the (2+5×(i−1))-th column is cyclically shifted in the downward direction by Q₁).

In addition, for example, in the (2+5×(i−1))-th column of the C matrix, the (1+5×(i−1))-th column is cyclically shifted in the downward direction by Q₂ (=2), and in the next (3+5×(i−1))-th column, the (1+5×(i−1))-th column is cyclically shifted in the downward direction by 2×Q₂ (=2×2) (the (2+5×(i−1))-th column is cyclically shifted in the downward direction by Q₂).

FIG. 24 is a diagram that illustrates the A matrix generated from the parity check matrix initial value table illustrated in FIG. 23.

In the A matrix illustrated in FIG. 24, according to the 1st row of the parity check matrix initial value table illustrated in FIG. 23, elements of rows #2 and #6 of a 1 (=1+5×(1−1))-st column are 1.

Then, in each of a 2 (=2+5×(1−1))-nd column to a 5 (=5+5×(1−1))-th column, an immediately previous column is cyclically shifted in the downward direction by Q₁=3.

In addition, in the A matrix illustrated in FIG. 24, according to the 2nd row of the parity check matrix initial value table illustrated in FIG. 23, elements of rows #2 and #10 of a 6 (=1+5×(2−1))-th column are 1.

Furthermore, in each of a 7 (=2+5×(2−1))-th column to a 10 (=5+5×(2−1))-th column, an immediately previous column is cyclically shifted in the downward direction by Q₁=3.

FIG. 25 is a diagram that illustrates the parity interleave of the B matrix.

The parity check matrix generating unit 613 (FIG. 18) generates the A matrix using the parity check matrix initial value table and arranges the B matrix having the staircase structure neighboring to the right side of the A matrix. Then, the parity check matrix generating unit 613 regards the B matrix as the parity matrix and performs parity interleave such that adjacent elements “1” of the B matrix having the staircase structure are separate from each other in the row direction by the unit size P=5.

FIG. 25 illustrates the A matrix and the B matrix after the parity interleave of the B matrix.

FIG. 26 is a diagram that illustrates the C matrix generated from the parity check matrix initial value table illustrated in FIG. 23.

In the C matrix illustrated in FIG. 26, according to the 1st row of the parity check matrix initial value table illustrated in FIG. 23, an element of a row #18 of a 1 (=1+5×(1−1))-st column of the parity check matrix is “1”.

In addition, in each of a 2 (=2+5×(1−1))-nd column to a 5 (=5+5×(1×1))-th column of the C matrix, an immediately previous column is cyclically shifted in the downward direction by Q₂=2.

Furthermore, in the C matrix illustrated in FIG. 26, according to the 2nd to 5th rows of the parity check matrix initial value table illustrated in FIG. 23, elements of a row #19 of a 6 (=1+5×(2−1))-th column of the parity check matrix, a row #22 of an 11 (=1+5×(3−1))-th column, a row #19 of a 16 (=1+5×(4−1))-th column, and a row #15 of a 21 (=1+5×(5−1))-th column are “1”s.

In addition, in each of the 7 (=2+5×(2−1))-th column to the 10 (=5+5×(2−1))-th column, each of a 12 (=2+5×(3−1))-th column to a 15 (=5+5×(3−1))-th column, each of a 17 (=2+5×(4−1))-th column to a 20 (=5+5×(4−1))-th column, and each of a 22 (=2+5×(5−1))-nd column to a 25 (=5+5×(5−1))-th column, an immediately previous column is cyclically shifted in the downward direction by Q₂=2.

The parity check matrix generating unit 613 (FIG. 18) generates the C matrix using the parity check matrix initial value table and arranges the C matrix below the A matrix and the B matrix (after the parity interleave thereof).

In addition, the parity check matrix generating unit 613 arranges the Z matrix neighboring to the right side of the B matrix and arranges the D matrix neighboring to the right side of the C matrix, thereby generating the parity check matrix illustrated in FIG. 26.

FIG. 27 is a diagram that illustrates parity interleave of the D matrix.

After generating the parity check matrix illustrated in FIG. 26, the parity check matrix generating unit 613 regards the D matrix as the parity matrix and performs the parity interleave (of only the D matrix) such that the elements “1” of odd-numbered rows and the next even-numbered rows of the D matrix of the unit matrix are separate from each other in the row direction by the unit size P (=5).

FIG. 27 illustrates the parity check matrix after the parity interleave of the D matrix is performed for the parity check matrix illustrated in FIG. 26.

The LDPC encoder 115 (the coding parity calculating unit 615 (FIG. 18) thereof) performs LDPC coding (generation of an LDPC code), for example, by using the parity check matrix illustrated in FIG. 27.

Here, the LDPC code generated using the parity check matrix illustrated in FIG. 27 is the LDPC code for which the parity interleave has been performed, and accordingly, it is unnecessary for the parity interleaver 23 (FIG. 9) to perform the parity interleave for the LDPC code generated using the parity check matrix illustrated in FIG. 27.

FIG. 28 is a diagram that illustrates the parity check matrix acquired by performing column permutation as parity deinterleave for restoring the parity interleave to an original state for the B matrix, a portion of the C matrix (a portion of the C matrix arranged below the B matrix) and the D matrix of the parity check matrix illustrated in FIG. 27.

The LDPC encoder 115 can perform LDPC coding (generation of an LDPC code) using the parity check matrix illustrated in FIG. 28.

In a case where the LDPC coding is performed using the parity check matrix illustrated in FIG. 28, the LDPC code for which the parity interleave is not performed is acquired according to the LDPC coding. Thus, in a case where the LDPC coding is performed using the parity check matrix illustrated in FIG. 28, the parity interleaver 23 (FIG. 9) performs the parity interleave.

FIG. 29 is a diagram that illustrates a transformed parity check matrix acquired by performing the row permutation for the parity check matrix illustrated in FIG. 27.

As will be described later, the transformed parity check matrix is a matrix represented by a combination of a unit matrix of P×P, a quasi unit matrix acquired by setting one or more “1”s to “0” in the unit matrix, a shift matrix acquired by cyclically shifting the unit matrix or the quasi unit matrix, a sum matrix that is a sum of two or more matrices among the unit matrix, the quasi unit matrix, and the shift matrix, and a zero matrix of P×P.

By using the transformed parity check matrix for decoding an LDPC code, an architecture, which will be described later, for performing P check node operations and P variable node operations at the same time can be employed in decoding the LDPC code.

<New LDPC Code>

Meanwhile, the standardization of digital television broadcasting of terrestrial waves called ATSC 3.0 is currently formulated.

Thus, a new LDPC code (hereinafter also referred to as a new LDPC code) that can be used in ATSC 3.0 and other data transmission will be described.

As the new LDPC code, for example, an LDPC code of the DVB type or an LDPC code of the ETRI type having a unit size P of 360, similar to DVB-T.2 or the like, corresponding to the parity check matrix having a cyclic structure may be employed.

The LDPC encoder 115 (FIGS. 8 and 18) can perform LDPC coding for generating a new LDPC code using a parity check matrix acquired from the parity check matrix initial value table of the new LDPC code having a code length N of 16 kbits or 64 kbits and a coding rate r of one of 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15 as below.

In this case, the storage unit 602 of the LDPC encoder 115 (FIG. 8) stores the parity check matrix initial value table of the new LDPC code.

FIG. 30 is a diagram that illustrates an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 16 kbits and a coding rate r of 8/15 (hereinafter, also referred to as Sony code of (16 k, 8/15)), proposed by the applicant of the present application.

FIG. 31 is a diagram that illustrates an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code in which the code length N is 16 kbits, and the coding rate r is 10/15 (hereinafter, also referred to as Sony code (16 k, 10/15)), proposed by the applicant of the present application.

FIG. 32 is a diagram that illustrates an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 16 kbits and a coding rate r of 12/15 (hereinafter, also referred to as Sony code of (16 k, 12/15)), proposed by the applicant of the present application.

FIGS. 33, 34, and 35 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 7/15 (hereinafter, also referred to as Sony code of (64 k, 7/15)), proposed by the applicant of the present application.

Note that FIG. 34 is a diagram following FIG. 33, and FIG. 35 is a diagram following FIG. 34.

FIGS. 36, 37, and 38 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 9/15 (hereinafter, also referred to as Sony code of (64 k, 9/15)), proposed by the applicant of the present application.

Note that FIG. 37 is a diagram following FIG. 36, and FIG. 38 is a diagram following FIG. 37.

FIGS. 39, 40, 41 and 42 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 11/15 (hereinafter, also referred to as Sony code of (64 k, 11/15)), proposed by the applicant of the present application.

Note that FIG. 40 is a diagram following FIG. 39, FIG. 41 is a diagram following FIG. 40, and FIG. 42 is a diagram following FIG. 41.

FIGS. 43, 44, 45, and 46 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 13/15 (hereinafter, also referred to as Sony code of (64 k, 13/15)), proposed by the applicant of the present application.

Note that FIG. 44 is a diagram following FIG. 43, FIG. 45 is a diagram following FIG. 44, and FIG. 46 is a diagram following FIG. 45.

FIGS. 47 and 48 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 6/15 (hereinafter, also referred to as Samsung code of (64 k, 6/15)), proposed by Samsung.

Note that FIG. 48 is a diagram following FIG. 47

FIGS. 49, 50, and 51 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 8/15 (hereinafter, also referred to as Samsung code of (64 k, 8/15)), proposed by Samsung.

Note that FIG. 50 is a diagram following FIG. 49, and FIG. 51 is a diagram following FIG. 50.

FIGS. 52, 53, and 54 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 12/15 (hereinafter, also referred to as Samsung code of (64 k, 12/15)), proposed by Samsung.

Note that FIG. 53 is a diagram following FIG. 52, and FIG. 54 is a diagram following FIG. 53.

FIG. 55 is a diagram that illustrates an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 16 kbits and a coding rate r of 6/15 (hereinafter, also referred to as LGE code of (16 k, 6/15)), proposed by LGE.

FIG. 56 is a diagram that illustrates an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 16 kbits and a coding rate r of 7/15 (hereinafter, also referred to as LGE code of (16 k, 7/15)), proposed by LGE.

FIG. 57 is a diagram that illustrates an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 16 kbits and a coding rate r of 9/15 (hereinafter, also referred to as LGE code of (16 k, 9/15)), proposed by LGE.

FIG. 58 is a diagram that illustrates an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 16 kbits and a coding rate r of 11/15 (hereinafter, also referred to as LGE code of (16 k, 11/15)), proposed by LGE.

FIG. 59 is a diagram that illustrates an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 16 kbits and a coding rate r of 13/15 (hereinafter, also referred to as LGE code of (16 k, 13/15)), proposed by LGE.

FIGS. 60, 61, and 62 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 10/15 (hereinafter, also referred to as LGE code of (64 k, 10/15)), proposed by LGE.

Note that FIG. 61 is a diagram following FIG. 60, and FIG. 62 is a diagram following FIG. 61.

FIGS. 63, 64, and 65 are diagrams that illustrate an example of a parity check matrix initial value table of the DVB type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 9/15 (hereinafter, also referred to as NERC code of (64 k, 9/15)), proposed by NERC.

Note that FIG. 64 is a diagram following FIG. 63, and FIG. 65 is a diagram following FIG. 64.

FIG. 66 is a diagram that illustrates an example of a parity check matrix initial value table of the ETRI type for a parity check matrix of a new LDPC code having a code length N of 16 kbits and a coding rate r of 5/15 (hereinafter, also referred to as ETRI code of (16 k, 5/15)), proposed by CRC/ETRI.

FIGS. 67 and 68 are diagrams that illustrate an example of a parity check matrix initial value table of the ETRI type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 5/15 (hereinafter, also referred to as ETRI code of (64 k, 5/15)), proposed by CRC/ETRI.

Note that FIG. 68 is a diagram following FIG. 67.

FIGS. 69 and 70 are diagrams that illustrate an example of a parity check matrix initial value table of the ETRI type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 6/15 (hereinafter, also referred to as ETRI code of (64 k, 6/15)), proposed by CRC/ETRI.

Note that FIG. 70 is a diagram following FIG. 69.

FIGS. 71 and 72 are diagrams that illustrate an example of a parity check matrix initial value table of the ETRI type for a parity check matrix of a new LDPC code having a code length N of 64 kbits and a coding rate r of 7/15 (hereinafter, also referred to as ETRI code of (64 k, 7/15)), proposed by CRC/ETRI.

Note that FIG. 72 is a diagram following FIG. 71.

Among the new LDPC codes, particularly, the Sony code is an LDPC code having good performance.

Here, the LDPC code of good performance is an LDPC code that is acquired from an appropriate parity check matrix H.

The appropriate parity check matrix H, for example, is a parity check matrix satisfying a predetermined condition that a bit error rate (BER) (and a frame error rate (FER)) becomes smaller when an LDPC code acquired from the parity check matrix H is transmitted with low E_(s)/N₀ or E_(b)/N_(o)(signal-to-noise power ratio per bit).

For example, the appropriate parity check matrix H can be acquired by performing simulation of measuring a BER at the time of transmitting LDPC codes acquired from various parity check matrices satisfying a predetermined condition at a low E_(s)/N_(o).

As a predetermined condition to be satisfied by the appropriate parity check matrix H, for example, an analysis result acquired by a code performance analysis method called density evolution (Density Evolution) is good, and there is no loop of elements of “1” called cycle-4, or the like.

Here, in the information matrix H_(A), it is known that the decoding performance of an LDPC code is degraded in a case where elements of “1” are densely formed like in case of cycle-4. For this reason, it is requested that there is no cycle-4 as the predetermined condition to be satisfied by the appropriate parity check matrix H.

Note that the predetermined condition to be satisfied by the appropriate parity check matrix H can be appropriately determined from the viewpoints of the improvement in the decoding performance of an LDPC code, the facilitation (simplification) of the decoding process of an LDPC code, and the like.

FIGS. 73 and 74 are diagrams that illustrate the density evolution acquiring an analysis result as a predetermined condition to be satisfied by the appropriate parity check matrix H.

The density evolution is a code analysis method for calculating the expectation value of an error probability of the entire LDPC code (ensemble) having a code length N of ∞ that is characterized by a degree sequence described later.

For example, as the dispersion value of noise is gradually increased from 0 on the AWGN channel, while, first, the expectation value of the error probability of a certain ensemble is “0”. However, when the dispersion value of noise becomes a certain threshold or more, the expectation value is not “0”.

According to the density evolution, by comparing the thresholds of the dispersion values of noise (hereinafter, also referred to as a performance threshold) for which the expectation value of the error probability is not “0”, it can be determined whether the performance (the appropriateness of the parity check matrix) of the ensemble is good or bad.

Note that, for a specific LDPC code, when an ensemble to which the LDPC code belongs is determined, and the density evolution is performed for the ensemble, rough performance of the LDPC code can be predicted.

Accordingly, in a case where an ensemble of good performance is found, an LDPC code of good performance can be found from among LDPC codes that belong to the ensemble.

Here, the degree sequence described above represents at what percentage a variable node or a check node having the weight of each value is present for the code length N of an LDPC code.

For example, a regular (3, 6) LDPC code having a coding rate of 1/2 belongs to an ensemble that is characterized by a degree sequence in which the weight (column weight) of all the variable nodes is 3, and the weight (row weight) of all the check nodes is 6.

FIG. 73 illustrates a Tanner graph of such an ensemble.

In the Tanner graph illustrated in FIG. 73, there are N variable nodes represented as circles (mark “◯”) in the diagram wherein N is equal to the code length N, and there are N/2 check nodes represented as squares (mark “□”) wherein N/2 is equal to a multiplication value acquired by multiplying the code length N by the coding rate “1/2”.

Three branches (edges) are connected to each variable node, wherein three is equal to the column weight, and accordingly, there are a total of 3N branches connected to the N variable nodes.

In addition, six branches are connected to each check node wherein six is equal to the row weight, and accordingly, there are a total of 3N branches connected to the N/2 check nodes.

Furthermore, there is one interleaver in the Tanner graph illustrated in FIG. 73.

The interleaver randomly rearranges 3N branches connected to the N variable nodes and connects each branch after the rearrangement to one of 3N branches connected to the N/2 check nodes.

There are (3N)! (=(3N)×(3N−1)× . . . ×1) rearrangement patterns for the rearrangement of the 3N branches connected to the N variable nodes in the interleaver. Accordingly, an ensemble characterized by the degree sequence in which the weight of all the variable nodes is 3, and the weight of all the check nodes is 6 is a set of (3N)! LDPC codes.

In simulation for acquiring an LDPC code of good performance (appropriate parity check matrix), an ensemble of a multi-edge type is used in the density evolution.

In the multi-edge type, an interleaver through which the branches connected to the variable nodes and the branches connected to the check nodes pass is divided into a plurality of parts (multi edges), and, accordingly, the ensemble is more strictly characterized.

FIG. 74 illustrates an example of a Tanner graph of an ensemble of the multi-edge type.

In the Tanner graph illustrated in FIG. 74, there are two interleavers including the first interleaver and the second interleaver.

In addition, in the Tanner graph illustrated in FIG. 74, there are v1 variable nodes each having one branch connected to the first interleaver and no branch connected to the second interleaver, there are v2 variable nodes each having one branch connected to the first interleaver and two branches connected to the second interleaver, and there are v3 variable nodes each having no branch connected to the first interleaver and two branches connected to the second interleaver.

Furthermore, in the Tanner graph illustrated in FIG. 74, there are c1 check nodes each having two branches connected to the first interleaver and no branch connected to the second interleaver, there are c2 check nodes each having two branches connected to the first interleaver and two branches connected to the second interleaver, and there are c3 check nodes each having no branch connected to the first interleaver and three branches connected to the second interleaver.

Here, the density evolution and the mounting thereof, for example, are described in “On the Design of Low-Density Parity-Check Codes within 0.0045 dB of the Shannon Limit”, S. Y Chung, G. D. Forney, T. J. Richardson, R. Urbanke, IEEE Communications Leggers, VOL. 5, NO. 2, February 2001.

In simulation for acquiring a Sony code (a parity check matrix initial value table thereof), according to the density evolution of the multi-edge type, an ensemble for which a performance threshold that is E_(b)/N₀ (signal-to-noise power ratio per bit), at which the BER starts to fall (decrease), is a predetermined value or less is retrieved, and an LDPC code for which the BER in a case where one or more quadrature modulations such as QPSK are used is low is selected from among LDPC codes belonging to the ensemble as an LDPC code of good performance.

The parity check matrix initial value table of the Sony code is acquired through the simulation described above.

Thus, according to the Sony code acquired from the parity check matrix initial value table, excellent communication quality can be secured in data transmission.

FIG. 75 is a diagram that illustrates parity check matrices H (hereinafter, also referred to as “parity check matrices H of Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15)”) acquired from the parity check matrix initial value table of the Sony codes (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15).

Each of all the minimum cycle lengths of the parity check matrices H of the Sony codes (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15) has a value exceeding cycle-4, and thus there is no cycle 4 (a loop of elements of “1” having a loop length of 4). Here, the minimum cycle length (girth) represents a minimum value of a length (a loop length) of a loop configured by elements of “1” in the parity check matrix H.

In addition, a performance threshold of the Sony code of (16 k, 8/15) is set to 0.805765, a performance threshold of the Sony code of (16 k, 10/15) is set to 2.471011, and a performance threshold of the Sony code of (16 k, 12/15) is set to 4.269922.

The column weight is set to X1 for KX1 columns of the parity check matrices H of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15) starting from the 1st column, the column weight is set to X2 for the following KX2 columns, the column weight is set to Y1 for the following KY1 columns, the column weight is set to Y2 for the following KY2 columns, the column weight is set to 2 for the following (M−1) columns, and the column weight is set to 1 for the last column.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N (=16200 bits) of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15).

In the parity check matrices H of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15), the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as represented in FIG. 75.

In the parity check matrices H of the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15), similarly to the parity check matrix described above with reference to FIGS. 12 and 13, a column disposed on a further head side (the left side) tends to have a higher column weight, and thus a code bit of the Sony code disposed on a further head side tends to be more resistant against an error (have resistance against an error).

According to the simulation conducted by the applicant of the present application, an excellent BER/FER is acquired for the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15), and thus excellent communication quality can be secured in data transmission using the Sony codes of (16 k, 8/15), (16 k, 10/15), and (16 k, 12/15).

FIG. 76 is a diagram that illustrates parity check matrices H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15).

Each of all the minimum cycle lengths of the parity check matrices H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15) has a value exceeding cycle-4, and thus there is no cycle-4.

In addition, a performance threshold value of the Sony code of (64 k, 7/15) is set to −0.093751, a performance threshold value of the Sony code of (64 k, 9/15) is set to 1.658523, a performance threshold value of the Sony code of (64 k, 11/15) is set to 3.351930, and a performance threshold value of the Sony code of (64 k, 13/15) is set to 5.301749.

The column weight is set to X1 for KX1 columns of the parity check matrices H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15) starting from the 1st column, the column weight is set to X2 for the following KX2 columns, the column weight is set to Y1 for the following KY1 columns, the column weight is set to Y2 for the following KY2 columns, the column weight is set to 2 for the following (M−1) columns, and the column weight is set to 1 for the last column.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=64800 bits of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15).

In the parity check matrices H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15), the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as illustrated in FIG. 76.

In the parity check matrices H of the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and, (64 k, 13/15), similarly to the parity check matrix described above with reference to FIGS. 12 and 13, a column disposed on a further head side (the left side) tends to have a higher column weight, and thus a code bit of the Sony code disposed on a further front side tends to be more resistant against an error.

According to the simulation conducted by the applicant of the present application, an excellent BER/FER is acquired for the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15), and thus excellent communication quality can be secured in data transmission using the Sony codes of (64 k, 7/15), (64 k, 9/15), (64 k, 11/15), and (64 k, 13/15).

FIG. 77 is a diagram that illustrates parity check matrices H of the Samsung codes of (64 k, 6/15), (64 k, 8/15), and (64 k, 12/15).

The column weight is set to X1 for KX1 columns of the parity check matrices H of the Samsung codes of (64 k, 6/15), (64 k, 8/15), and (64 k, 12/15) starting from the 1st column, the column weight is set to X2 for the following KX2 columns, the column weight is set to Y1 for the following KY1 columns, the column weight is set to Y2 for the following KY2 columns, the column weight is set to 2 for the following (M−1) columns, and the column weight is set to 1 for the last column.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=64800 bits of the Samsung codes of (64 k, 6/15), (64 k, 8/15), and (64 k, 12/15).

In the parity check matrices H of the Samsung codes of (64 k, 6/15), (64 k, 8/15), and (64 k, 12/15), the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as illustrated in FIG. 77.

FIG. 78 is a diagram that illustrates parity check matrices H of the LGE codes of (16 k, 6/15), (16 k, 7/15), (16 k, 9/15), (16 k, 11/15), and (16 k, 13/15).

The column weight is set to X1 for KX1 columns of the parity check matrices H of the LGE codes of (16 k, 6/15), (16 k, 7/15), (16 k, 9/15), (16 k, 11/15), and (16 k, 13/15) starting from the 1st column, the column weight is set to X2 for the following KX2 columns, the column weight is set to Y1 for the following KY1 columns, the column weight is set to Y2 for the following KY2 columns, the column weight is set to 2 for the following (M−1) columns, and the column weight is set to 1 for the last column.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=16200 bits of the LGE codes of (16 k, 6/15), (16 k, 7/15), (16 k, 9/15), (16 k, 11/15), and (16 k, 13/15).

In the parity check matrices H of the LGE codes of (16 k, 6/15), (16 k, 7/15), (16 k, 9/15), (16 k, 11/15), and (16 k, 13/15), the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as illustrated in FIG. 78.

FIG. 79 is a diagram that illustrates a parity check matrix H of the LGE code of (64 k, 10/15).

The column weight is set to X1 for KX1 columns of the parity check matrix H of the LGE code of (64 k, 10/15) starting from the 1st column, the column weight is set to X2 for the following KX2 columns, the column weight is set to Y1 for the following KY1 columns, the column weight is set to Y2 for the following KY2 columns, the column weight is set to 2 for the following (M−1) columns, and the column weight is set to 1 for the last column.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=64800 bits of the LGE code of (64 k, 10/15).

In the parity check matrix H of the LGE code of (64 k, 10/15), the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as illustrated in FIG. 79.

FIG. 80 is a diagram that illustrates a parity check matrix H of the NERC code of (64 k, 9/15).

The column weight is set to X1 for KX1 columns of the parity check matrix H of the NERC code of (64 k, 9/15) starting from the 1st column, the column weight is set to X2 for the following KX2 columns, the column weight is set to Y1 for the following KY1 columns, the column weight is set to Y2 for the following KY2 columns, the column weight is set to 2 for the following (M−1) columns, and the column weight is set to 1 for the last column.

Here, KX1+KX2+KY1+KY2+M−1+1 is equal to the code length N=64800 bits of the NERC code of (64 k, 9/15).

In the parity check matrix H of the NERC code of (64 k, 9/15), the numbers KX1, KX2, KY1, KY2, and M of columns and column weights X1, X2, Y1, and Y2 are set as illustrated in FIG. 80.

FIG. 81 is a diagram that illustrates a parity check matrix H of the ETRI code of (16 k, 5/15).

For the parity check matrix H of the ETRI code of (16 k, 5/15), the parameter g=M₁ is 720.

In addition, for the ETRI code of (16 k, 5/15), since the code length N is 16200 and the coding rate r is 5/15, the information length K=N×r is 16200×5/15=5400, and the parity length M=N−K is 16200-5400=10800.

Furthermore, the parameter M₂=M−M₁=N−K−g is 10800−720=10080.

Thus, the parameter Q₁=M₁/P is 720/360=2, and the parameter Q₂=M₂/P is 10080/360=28.

FIG. 82 is a diagram that illustrates parity check matrices H of ETRI codes of (64 k, 5/15), (64 k, 6/15), and (64 k, 7/15).

For the parity check matrices H of the ETRI codes of (64 k, 5/15), (64 k, 6/15), and (64 k, 7/15), the parameters g=M₁, M₂, Q₁, and Q₂ are set as illustrated in FIG. 82.

<Constellation>

FIGS. 83 to 93 are diagrams that illustrate examples of constellation types employed in the transmission system illustrated in FIG. 7.

In the transmission system illustrated in FIG. 7, for example, a constellation to be employed in ATSC 3.0 may be employed.

In ATSC 3.0, for MODCOD that is a combination of a modulation scheme and an LDPC code, a constellation to be used in the MODCOD is set.

Here, in ATSC 3.0, five types of modulation schemes including QPSK, 16 QAM, 64 QAM, 256 QAM, and 1024 QAM (1 k QAM) are planned to be employed.

In addition, in ATSC 3.0, for each of two types of code length N including 16 kbits and 64 kbits, LDPC codes of nine types of coding rates r including 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15, in other words, 9×2=18 types of LDPC codes are planned to be employed.

In ATSC 3.0, 18 types of LDPC codes are classified into 9 types on the basis of the coding rate r (regardless of the code length N), and 45 (=9×5) types of combinations of the 9 types of LDPC codes (LDPC codes having coding rates r of 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15) and the five types of modulation schemes are planned to be employed as the MODCOD.

In addition, in the ATSC 3.0, for one MODCOD, one or more constellations are planned to be employed.

The constellations include uniform constellations (UC) in which the arrangement of signal points is uniform and non-uniform constellations (NUC) in which the arrangement of signal points is not uniform.

In addition, examples of NUCs include a constellation called a 1-dimensional M²-QAM non-uniform constellation (1D NUC) and a constellation called a 2-dimensional QQAM non-uniform constellation (2D NUC).

Generally, the 1D NUC has a BER that is better than that of the UC, and the 2D NUC has a BER that is better than that of the 1D NUC.

As the constellation of the QPSK, the UC is employed. In addition, as the constellation of the 16 QAM, the 64 QAM, or the 256 QAM, for example, the 2D NUC is employed, and, as the constellation of the 1024 QAM, for example, the 1D NUC is employed.

Hereinafter, a constellation of the NUC used in the MODCOD having a modulation scheme in which an m-bit symbol is mapped into one of 2^(m) signal points and a coding rate of an LDPC code of r will be also referred to as NUC_2^(m)_r (here, m=4, 6, 8, and 10).

For example, “NUC_16_6/15” represents a constellation of the NUC used in the MODCOD having a modulation scheme of 16 QAM and a coding rate r of the LDPC code of 6/15.

In ATSC 3.0, in a case where the modulation scheme is the QPSK, for 9 types of coding rates r of the LDPC code, the same constellation is planned to be used.

In addition, in ATSC 3.0, in a case where the modulation scheme is the 16 QAM, the 64 QAM, or the 256 QAM, a different constellation of the 2D NUC is planned to be used for each of 9 types of coding rates r of the LDPC code.

Furthermore, in ATSC 3.0, in a case where the modulation scheme is the 1024 QAM, a different constellation of the 1D NUC is planned to be used for each of 9 types of coding rates r of the LDPC code.

Thus, in ATSC 3.0, for the QPSK, one type of constellation is planned to be prepared, for each of the 16 QAM, the 64 QAM, and the 256 QAM, 9 types of constellations of the 2D NUC are planned to be prepared, and, for the 1024 QAM, 9 types of constellations of the 1D NUC are planned to be prepared.

FIG. 83 is a diagram that illustrates an example of a constellation of the 2D NUC for each of 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15) of LDPC codes in a case where the modulation scheme is the 16 QAM.

FIG. 84 is a diagram that illustrates an example of a constellation of the 2D NUC for each of 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of LDPC codes in a case where the modulation scheme is the 64 QAM.

FIG. 85 is a diagram that illustrates an example of a constellation of the 2D NUC for each of 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15) of LDPC codes in a case where the modulation scheme is the 256 QAM.

FIG. 86 is a diagram that illustrates an example of a constellation of the 1D NUC for each of 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15) of LDPC codes in a case where the modulation scheme is 1024 QAM.

In FIGS. 83 to 86, the horizontal axis and the vertical axis are respectively an I axis and a Q axis, and Re{x₁} and Im{x₁} respectively represent a real part and an imaginary part of a signal point x₁ as coordinates of the signal point x₁.

In addition, in FIGS. 83 to 86, a numerical value written after “for CR” represents the coding rate r of the LDPC code.

FIG. 87 is a diagram that illustrates an example of coordinates of a signal point of the UC that is used in common to 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of LDPC codes in a case where the modulation scheme is the QPSK.

In FIG. 87, “Input cell word y” represents a 2-bit symbol that is mapped into a UC of the QPSK, and “Constellation point z_(q)” represents the coordinates of a signal point z_(q). In addition, an index q of the signal point z_(q) represents a discrete time between symbols (a time interval between a certain symbol and a next symbol).

In FIG. 87, the coordinates of the signal point z_(q) are represented in the form of a complex number, and i represents an imaginary unit (√(−1)).

FIG. 88 is a diagram that illustrates an example of the coordinates of a signal point of the 2D NUC used for 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15) of the LDPC codes in a case where the modulation scheme is the 16 QAM.

FIG. 89 is a diagram that illustrates an example of the coordinates of a signal point of the 2D NUC used for 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, and 13/15) of LDPC codes in a case where the modulation scheme is the 64 QAM.

FIGS. 90 and 91 are diagrams that illustrate an example of the coordinates of a signal point of the 2D NUC used for 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of LDPC codes in a case where the modulation scheme is the 256 QAM.

In FIGS. 88 to 91, NUC_2^(m)_r represents the coordinates of a signal point of the 2D NUC used in a case where the modulation scheme is the 2^(m) QAM, and the coding rate of LDPC codes is r.

In FIGS. 88 to 91, similarly to the case illustrated in FIG. 87, the coordinates of the signal point z_(q) are represented in the form of a complex number, and i represents an imaginary unit.

In FIGS. 88 to 91, w #k represents the coordinates of a signal point in a first quadrant of the constellation.

In the 2D NUC, a signal point in a second quadrant of the constellation is arranged at a position acquired by moving the signal point disposed in the first quadrant symmetrically with respect to the Q axis, and a signal point in a third quadrant of the constellation is arranged at a position acquired by moving the signal point disposed in the first quadrant symmetrically with respect to the origin. In addition, a signal point in a fourth quadrant of the constellation is arranged at a position acquired by moving the signal point disposed in the first quadrant symmetrically with respect to the I axis.

Here, in a case where the modulation scheme is the 2^(m) QAM, m bits are configured as one symbol, and one symbol is mapped into a signal point corresponding to the symbol.

The m-bit symbol, for example, is represented by an integer value of 0 to 2^(m)−1, and, when b=2^(m)/4, symbols y(0), y(1), . . . , y(2^(m)−1) represented by the integer value of 0 to 2^(m)−1 can be classified into four symbols of y(0) to y(b−1), y(b) to y(2b−1), y(2b) to y(3b−1), and y(3b) to y(4b−1).

In FIGS. 88 to 91, a suffix k of w #k takes an integer value in the range of 0 to b−1, and w #k represents the coordinates of a signal point corresponding to a symbol y(k) in the range of the symbols y(0) to y(b−1).

In addition, the coordinates of a signal point corresponding to a symbol y(k+b) in the range of the symbols y(b) to y(2b−1) are represented by −conj (w #k), and the coordinates of a signal point corresponding to a symbol y(k+2b) in the range of the symbols y(2b) to y(3b−1) are represented by conj (w #k). Furthermore, the coordinates of a signal point corresponding to a symbol y(k+3b) in the range of the symbols y(3b) to y(4b−1) are represented by −w #k.

Here, conj (w #k) represents a complex conjugate of w #k.

For example, in a case where the modulation scheme is the 16 QAM, the symbols y(0), y(1), . . . , y(15) of m=4 bits are classified into four symbols of y(0) to y(3), y(4) to y(7), y(8) to y(11), and y(12) to y(15) with b=2⁴/4=4.

Then, among the symbols y(0) to y(15), for example, the symbol y(12) is a symbol y(k+3b)=y(0+3×4) in the range of the symbols y(3b) to y(4b−1), and k=0. Accordingly, the coordinates of the signal point corresponding to the symbol y(12) are −w #k=−w0.

Now, when the coding rate r of the LDPC code, for example, is 9/15, by referring to FIG. 88, in a case where the modulation scheme is the 16 QAM, and the coding rate r is 9/15, w0 of (NUC_16_9/15) is 0.4967+1.1932i. Accordingly, the coordinates −w0 of the signal point corresponding to the symbol y(12) are −(0.4967+1.1932i).

FIG. 92 is a diagram that illustrates an example of the coordinates of a signal point of the 1D NUC used for 9 types of coding rates r (=5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12, 15, and 13/15) of LDPC codes in a case where the modulation scheme is the 1024 QAM.

In FIG. 92, a column of NUC_1k_r represents a value taken by u #k representing the coordinates of a signal point of the 1D NUC used in a case where the modulation scheme is the 1024 QAM, and the coding rate of LDPC codes is r.

u #k represents the real part Re(z_(q)) and the imaginary part Im(z_(q)) of a complex number as the coordinates of the signal point z_(q) of the 1D NUC.

FIG. 93 is a diagram that illustrates a relation between the symbol y and u #k as each of the real part Re(z_(q)) and the imaginary part Im(z_(q)) of the complex number representing the coordinates of the signal point z_(q) of the 1D NUC corresponding to the symbol y.

Now, a 10-bit symbol y of the 1024 QAM is assumed to be represented by y_(0,q), y_(1,q), y_(2,q), y_(3,q), y_(4,q), y_(5,q), y_(6,q), y_(7,q), y_(8,q), and y_(9,q) from the first bit (the most significant bit).

A of FIG. 93 illustrates a correspondence relation between 5 odd-numbered bits y_(0,q), y_(2,q), y_(4,q), y_(6,q), y_(8,q) of the symbol y and u #k representing the real part Re(z_(q)) (of the coordinates) of a signal point z_(q) corresponding to the symbol y.

B of FIG. 93 illustrates a correspondence relation between 5 even-numbered bits y_(1,q), y_(3,q), y_(5,q), y_(7,q), and y_(9,q) of the symbol y and u #k representing the imaginary part Im(z_(q)) (of the coordinates) of a signal point z_(q) corresponding to the symbol y.

For example, in a case where the 10-bit symbol y=(y_(0,q), y_(1,q), y_(2,q), y_(3,q), y_(4,q), y_(5,q), y_(6,q), y_(7,q), y_(8,q), y_(9,q)) of the 1024 QAM is (0, 0, 1, 0, 0, 1, 1, 1, 0, 0), the 5 odd-numbered bits (y_(0,q), y_(2,q), y_(4,q), y_(6,q), y_(8,q)) are (0, 1, 0, 1, 0), and the 5 even-numbered bits (y_(1,q), y_(3,q), y_(5,q), y_(7,q), and y_(9,q)) are (0, 0, 1, 1, 0).

In A of FIG. 93, the 5 odd-numbered bits (0, 1, 0, 1, 0) are associated with u3, and thus, the real part Re(z_(q)) of the signal point z_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) is u3.

In addition, in B of FIG. 93, the 5 even-numbered bits (0, 0, 1, 1, 0) are associated with u11, and thus, the imaginary part Im(z_(q)) of the signal point z_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) is u11.

Meanwhile, in a case where the coding rate r of the LDPC code, for example, is 7/15, by referring to FIG. 92 described above, for the 1D NUC (NUC_1 k_7/15) used in a case where the modulation scheme is the 1024 QAM and the coding rate r of LDPC codes is 7/15, u3 is 1.1963, and u11 is 6.9391.

Accordingly, the real part Re(z_(q)) of the signal point z_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) is u3 (=1.1963), and Im(z_(q)) is u11 (=6.9391). As a result, the coordinates of the signal point z_(q) corresponding to the symbol y=(0, 0, 1, 0, 0, 1, 1, 1, 0, 0) are represented by 1.1963+6.9391i.

Note that the signal points of the 1D NUC are arranged in a grid form on a straight line parallel to the I axis or a straight line parallel to the Q axis. However, an interval between the signal points is not constant. In addition, in the transmission of the signal point (the mapped data), average power of the signal points on the constellation is normalized. When a root mean square value of absolute values of all the signal points (the coordinates thereof) on the constellation is represented by P_(ave), the normalization is performed by multiplying each signal point z_(q) on the constellation by a reciprocal 1/(√P_(ave)) of the square root √P_(ave) of the root mean square value P_(ave).

According to the constellations described above with reference to FIGS. 83 to 93, it is confirmed that an excellent error rate is acquired.

<Block Interleaver 25>

FIG. 94 is a block diagram that illustrates a configuration example of the block interleaver 25 illustrated in FIG. 9.

The block interleaver 25 includes a storage area called a part 1 and a storage area called a part 2.

Each of the parts 1 and 2 is configured by aligning columns as storage areas each storing one bit in the row (horizontal) direction and storing a predetermined number of bits in the column (vertical) direction that correspond to the same number C as the number m of bits of a symbol in the row direction.

When the number of bits (hereinafter, also referred to as apart column length) that are stored in the column direction by the column of the part 1 is represented by R1, and the part column length of the column of the part 2 is represented by R2, (R1+R2)×C is equal to the code length N (64800 bits or 16200 bits in the present embodiment) of an LDPC code that is a block interleave target.

In addition, the part column length R1 is equal to a multiple of 360 bits that corresponds to the unit size P, and the part column length R2 is equal to a remainder acquired when a sum (hereinafter, also referred to as a column length) R1+R2 of the part column length R1 of the part 1 and the part column length R2 of the part 2 is divided by 360 bits corresponding to the unit size P.

Here, the column length R1+R2 is equal to a value acquired by dividing the code length N of the LDPC code that is the block interleave target by the number m of bits of the symbol.

For example, in a case where 16 QAM is employed as the modulation scheme for the LDPC code of which the code length N is 16200 bits, the number m of bits of the symbol is 4 bits, and accordingly, the column length R1+R2 is 4050 (=16200/4) bits.

In addition, since a remainder acquired when the column length R1+R2=4050 is divided by 360 bits used as the unit size P is 90, the part column length R2 of the part 2 is 90 bits.

Furthermore, the part column length R1 of the part 1 is R1+R2−R2=4050−90=3960 bits.

FIG. 95 is a diagram that illustrates the number C of columns of the parts 1 and 2 and the part column lengths (the number of rows) R1 and R2 for a combination of the code length N and the modulation scheme.

FIG. 95 illustrates the number C of columns of the parts 1 and 2 and the part column lengths R1 and R2 for combinations of LDPC codes in a case where the LDPC codes respectively have code lengths N of 16200 bits and 64800 bits and the modulation schemes of QPSK, 16 QAM, 64 QAM, 256 QAM, and 1024 QAM.

FIG. 96 is a diagram that illustrates the block interleave performed by the block interleaver 25 illustrated in FIG. 94.

The block interleaver 25 performs the block interleave by writing and reading LDPC codes for the parts 1 and 2.

In other words, in the block interleave, as illustrated in A of FIG. 96, writing of code bits of LDPC codes of one code word in the downward direction (in the column direction) from the top of the columns of the part 1 is performed from the left side toward a rightward column.

Then, when the writing of the code bits is completed up to the bottom of the rightmost column (C-th column) of the columns of the part 1, writing of the remaining code bits in the downward direction (in the column direction) from the top of the column of the part 2 is performed from the left side toward a rightward column.

Thereafter, when the writing of the code bits is completed up to the bottom of the rightmost column (C-th column) of the columns of the part 2, as illustrated in B of FIG. 96, the code bits are read from the 1st rows of all the C columns of the part 1 in the row direction in units of C=m bits.

Then, the reading of the code bits from all the C columns of the part 1 is sequentially performed toward a row disposed on the lower side, and, when the reading is completed up to an R1-th row that is the last row, the code bits are read from the 1st rows of all the C columns of the part 2 in the row direction in units of C=m bits.

The reading of the code bits from all the C columns of the part 2 is sequentially performed toward a row disposed on the lower side, and the reading is performed up to an R2-th row that is the last row.

As above, the code bits read from the parts 1 and 2 in units of m bits are supplied to the mapper 117 (FIG. 8) as the symbol.

<Group-Wise Interleave>

FIG. 97 is a diagram that illustrates group-wise interleave performed by the group-wise interleaver 24 illustrated in FIG. 9.

In the group-wise interleave, 360 bits of one segment are used as the bit group, wherein the LDPC code of one code word is divided into segments from the head in units of 360 bits that is equal to the unit size P, and the LDPC code of one code word is interleaved according to a predetermined pattern (hereinafter, also referred to as a GW pattern) in units of bit groups.

Here, when the LDPC code of one code word is segmented into the bit groups, an (i+1)-th bit group from the head will be also referred to as a bit group i.

In a case where the unit size P is 360, for example, the LDPC code of which the code length N is 1800 bits is segmented into 5 (=1800/360) bit groups of bit groups 0, 1, 2, 3, and 4. In addition, for example, the LDPC code of which the code length N is 16200 bits is segmented into 45 (=16200/360) bit groups of bit groups 0, 1, . . . , and 44, and the LDPC code of which the code length N is 64800 bits is segmented into 180 (=64800/360) bit groups of bit groups 0, 1, . . . , 179.

In addition, hereinafter, the GW pattern is assumed to be represented by a sequence of numbers indicating a bit group. For example, for a LDPC code of which the code length N is 1800 bits, for example, the GW patterns 4, 2, 0, 3, 1 represent that a sequence of bit groups 0, 1, 2, 3, and 4 is interleaved (rearranged) into a sequence of bit groups 4, 2, 0, 3, and 1.

The GW pattern can be set at least for each code length N of the LDPC code.

FIG. 98 is a diagram that illustrates a first example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 98, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

39, 47, 96, 176, 33, 75, 165, 38, 27, 58, 90, 76, 17, 46, 10, 91, 133, 69, 171, 32, 117, 78, 13, 146, 101, 36, 0, 138, 25, 77, 122, 49, 14, 125, 140, 93, 130, 2, 104, 102, 128, 4, 111, 151, 84, 167, 35, 127, 156, 55, 82, 85, 66, 114, 8, 147, 115, 113, 5, 31, 100, 106, 48, 52, 67, 107, 18, 126, 112, 50, 9, 143, 28, 160, 71, 79, 43, 98, 86, 94, 64, 3, 166, 105, 103, 118, 63, 51, 139, 172, 141, 175, 56, 74, 95, 29, 45, 129, 120, 168, 92, 150, 7, 162, 153, 137, 108, 159, 157, 173, 23, 89, 132, 57, 37, 70, 134, 40, 21, 149, 80, 1, 121, 59, 110, 142, 152, 15, 154, 145, 12, 170, 54, 155, 99, 22, 123, 72, 177, 131, 116, 44, 158, 73, 11, 65, 164, 119, 174, 34, 83, 53, 24, 42, 60, 26, 161, 68, 178, 41, 148, 109, 87, 144, 135, 20, 62, 81, 169, 124, 6, 19, 30, 163, 61, 179, 136, 97, 16, 88

FIG. 99 is a diagram that illustrates a second example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 99, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

6, 14, 1, 127, 161, 177, 75, 123, 62, 103, 17, 18, 167, 88, 27, 34, 8, 110, 7, 78, 94, 44, 45, 166, 149, 61, 163, 145, 155, 157, 82, 130, 70, 92, 151, 139, 160, 133, 26, 2, 79, 15, 95, 122, 126, 178, 101, 24, 138, 146, 179, 30, 86, 58, 11, 121, 159, 49, 84, 132, 117, 119, 50, 52, 4, 51, 48, 74, 114, 59, 40, 131, 33, 89, 66, 136, 72, 16, 134, 37, 164, 77, 99, 173, 20, 158, 156, 90, 41, 176, 81, 42, 60, 109, 22, 150, 105, 120, 12, 64, 56, 68, 111, 21, 148, 53, 169, 97, 108, 35, 140, 91, 115, 152, 36, 106, 154, 0, 25, 54, 63, 172, 80, 168, 142, 118, 162, 135, 73, 83, 153, 141, 9, 28, 55, 31, 112, 107, 85, 100, 175, 23, 57, 47, 38, 170, 137, 76, 147, 93, 19, 98, 124, 39, 87, 174, 144, 46, 10, 129, 69, 71, 125, 96, 116, 171, 128, 65, 102, 5, 43, 143, 104, 13, 67, 29, 3, 113, 32, 165

FIG. 100 is a diagram that illustrates a third example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 100, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

103, 116, 158, 0, 27, 73, 140, 30, 148, 36, 153, 154, 10, 174, 122, 178, 6, 106, 162, 59, 142, 112, 7, 74, 11, 51, 49, 72, 31, 65, 156, 95, 171, 105, 173, 168, 1, 155, 125, 82, 86, 161, 57, 165, 54, 26, 121, 25, 157, 93, 22, 34, 33, 39, 19, 46, 150, 141, 12, 9, 79, 118, 24, 17, 85, 117, 67, 58, 129, 160, 89, 61, 146, 77, 130, 102, 101, 137, 94, 69, 14, 133, 60, 149, 136, 16, 108, 41, 90, 28, 144, 13, 175, 114, 2, 18, 63, 68, 21, 109, 53, 123, 75, 81, 143, 169, 42, 119, 138, 104, 4, 131, 145, 8, 5, 76, 15, 88, 177, 124, 45, 97, 64, 100, 37, 132, 38, 44, 107, 35, 43, 80, 50, 91, 152, 78, 166, 55, 115, 170, 159, 147, 167, 87, 83, 29, 96, 172, 48, 98, 62, 139, 70, 164, 84, 47, 151, 134, 126, 113, 179, 110, 111, 128, 32, 52, 66, 40, 135, 176, 99, 127, 163, 3, 120, 71, 56, 92, 23, 20

FIG. 101 is a diagram that illustrates a fourth example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 101, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

139, 106, 125, 81, 88, 104, 3, 66, 60, 65, 2, 95, 155, 24, 151, 5, 51, 53, 29, 75, 52, 85, 8, 22, 98, 93, 168, 15, 86, 126, 173, 100, 130, 176, 20, 10, 87, 92, 175, 36, 143, 110, 67, 146, 149, 127, 133, 42, 84, 64, 78, 1, 48, 159, 79, 138, 46, 112, 164, 31, 152, 57, 144, 69, 27, 136, 122, 170, 132, 171, 129, 115, 107, 134, 89, 157, 113, 119, 135, 45, 148, 83, 114, 71, 128, 161, 140, 26, 13, 59, 38, 35, 96, 28, 0, 80, 174, 137, 49, 16, 101, 74, 179, 91, 44, 55, 169, 131, 163, 123, 145, 162, 108, 178, 12, 77, 167, 21, 154, 82, 54, 90, 177, 17, 41, 39, 7, 102, 156, 62, 109, 14, 37, 23, 153, 6, 147, 50, 47, 63, 18, 70, 68, 124, 72, 33, 158, 32, 118, 99, 105, 94, 25, 121, 166, 120, 160, 141, 165, 111, 19, 150, 97, 76, 73, 142, 117, 4, 172, 58, 11, 30, 9, 103, 40, 61, 43, 34, 56, 116

FIG. 102 is a diagram that illustrates a fifth example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 102, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

72, 59, 65, 61, 80, 2, 66, 23, 69, 101, 19, 16, 53, 109, 74, 106, 113, 56, 97, 30, 164, 15, 25, 20, 117, 76, 50, 82, 178, 13, 169, 36, 107, 40, 122, 138, 42, 96, 27, 163, 46, 64, 124, 57, 87, 120, 168, 166, 39, 177, 22, 67, 134, 9, 102, 28, 148, 91, 83, 88, 167, 32, 99, 140, 60, 152, 1, 123, 29, 154, 26, 70, 149, 171, 12, 6, 55, 100, 62, 86, 114, 174, 132, 139, 7, 45, 103, 130, 31, 49, 151, 119, 79, 41, 118, 126, 3, 179, 110, 111, 51, 93, 145, 73, 133, 54, 104, 161, 37, 129, 63, 38, 95, 159, 89, 112, 115, 136, 33, 68, 17, 35, 137, 173, 143, 78, 77, 141, 150, 58, 158, 125, 156, 24, 105, 98, 43, 84, 92, 128, 165, 153, 108, 0, 121, 170, 131, 144, 47, 157, 11, 155, 176, 48, 135, 4, 116, 146, 127, 52, 162, 142, 8, 5, 34, 85, 90, 44, 172, 94, 160, 175, 75, 71, 18, 147, 10, 21, 14, 81

FIG. 103 is a diagram that illustrates a sixth example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 103, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

8, 27, 7, 70, 75, 84, 50, 131, 146, 99, 96, 141, 155, 157, 82, 57, 120, 38, 137, 13, 83, 23, 40, 9, 56, 171, 124, 172, 39, 142, 20, 128, 133, 2, 89, 153, 103, 112, 129, 151, 162, 106, 14, 62, 107, 110, 73, 71, 177, 154, 80, 176, 24, 91, 32, 173, 25, 16, 17, 159, 21, 92, 6, 67, 81, 37, 15, 136, 100, 64, 102, 163, 168, 18, 78, 76, 45, 140, 123, 118, 58, 122, 11, 19, 86, 98, 119, 111, 26, 138, 125, 74, 97, 63, 10, 152, 161, 175, 87, 52, 60, 22, 79, 104, 30, 158, 54, 145, 49, 34, 166, 109, 179, 174, 93, 41, 116, 48, 3, 29, 134, 167, 105, 132, 114, 169, 147, 144, 77, 61, 170, 90, 178, 0, 43, 149, 130, 117, 47, 44, 36, 115, 88, 101, 148, 69, 46, 94, 143, 164, 139, 126, 160, 156, 33, 113, 65, 121, 53, 42, 66, 165, 85, 127, 135, 5, 55, 150, 72, 35, 31, 51, 4, 1, 68, 12, 28, 95, 59, 108

FIG. 104 is a diagram that illustrates a seventh example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 104, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179

FIG. 105 is a diagram that illustrates an eighth example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 105, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

11, 5, 8, 18, 1, 25, 32, 31, 19, 21, 50, 102, 65, 85, 45, 86, 98, 104, 64, 78, 72, 53, 103, 79, 93, 41, 82, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 4, 12, 15, 3, 10, 20, 26, 34, 23, 33, 68, 63, 69, 92, 44, 90, 75, 56, 100, 47, 106, 42, 39, 97, 99, 89, 52, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 6, 16, 14, 7, 13, 36, 28, 29, 37, 73, 70, 54, 76, 91, 66, 80, 88, 51, 96, 81, 95, 38, 57, 105, 107, 59, 61, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 0, 9, 17, 2, 27, 30, 24, 22, 35, 77, 74, 46, 94, 62, 87, 83, 101, 49, 43, 84, 48, 60, 67, 71, 58, 40, 55, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179

FIG. 106 is a diagram that illustrates a ninth example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 106, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

9, 18, 15, 13, 35, 26, 28, 99, 40, 68, 85, 58, 63, 104, 50, 52, 94, 69, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 8, 16, 17, 24, 37, 23, 22, 103, 64, 43, 47, 56, 92, 59, 70, 42, 106, 60, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 169, 175, 4, 1, 10, 19, 30, 31, 89, 86, 77, 81, 51, 79, 83, 48, 45, 62, 67, 65, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 170, 176, 6, 2, 0, 25, 20, 34, 98, 105, 82, 96, 90, 107, 53, 74, 73, 93, 55, 102, 111, 117, 123, 129, 135, 141, 147, 153, 159, 165, 171, 177, 14, 7, 3, 27, 21, 33, 44, 97, 38, 75, 72, 41, 84, 80, 100, 87, 76, 57, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 5, 11, 12, 32, 29, 36, 88, 71, 78, 95, 49, 54, 61, 66, 46, 39, 101, 91, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179

FIG. 107 is a diagram that illustrates a tenth example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 107, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

0, 14, 19, 21, 2, 11, 22, 9, 8, 7, 16, 3, 26, 24, 27, 80, 100, 121, 107, 31, 36, 42, 46, 49, 75, 93, 127, 95, 119, 73, 61, 63, 117, 89, 99, 129, 52, 111, 124, 48, 122, 82, 106, 91, 92, 71, 103, 102, 81, 113, 101, 97, 33, 115, 59, 112, 90, 51, 126, 85, 123, 40, 83, 53, 69, 70, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 4, 5, 10, 12, 20, 6, 18, 13, 17, 15, 1, 29, 28, 23, 25, 67, 116, 66, 104, 44, 50, 47, 84, 76, 65, 130, 56, 128, 77, 39, 94, 87, 120, 62, 88, 74, 35, 110, 131, 98, 60, 37, 45, 78, 125, 41, 34, 118, 38, 72, 108, 58, 43, 109, 57, 105, 68, 86, 79, 96, 32, 114, 64, 55, 30, 54, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179

FIG. 108 is a diagram that illustrates an 11th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 108, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

21, 11, 12, 9, 0, 6, 24, 25, 85, 103, 118, 122, 71, 101, 41, 93, 55, 73, 100, 40, 106, 119, 45, 80, 128, 68, 129, 61, 124, 36, 126, 117, 114, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 20, 18, 10, 13, 16, 8, 26, 27, 54, 111, 52, 44, 87, 113, 115, 58, 116, 49, 77, 95, 86, 30, 78, 81, 56, 125, 53, 89, 94, 50, 123, 65, 83, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 17, 1, 4, 7, 15, 29, 82, 32, 102, 76, 121, 92, 130, 127, 62, 107, 38, 46, 43, 110, 75, 104, 70, 91, 69, 96, 120, 42, 34, 79, 35, 105, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 19, 5, 3, 14, 22, 28, 23, 109, 51, 108, 131, 33, 84, 88, 64, 63, 59, 57, 97, 98, 48, 31, 99, 37, 72, 39, 74, 66, 60, 67, 47, 112, 90, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179

FIG. 109 is a diagram that illustrates a 12th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 109, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

12, 15, 2, 16, 27, 50, 35, 74, 38, 70, 108, 32, 112, 54, 30, 122, 72, 116, 36, 90, 49, 85, 132, 138, 144, 150, 156, 162, 168, 174, 0, 14, 9, 5, 23, 66, 68, 52, 96, 117, 84, 128, 100, 63, 60, 127, 81, 99, 53, 55, 103, 95, 133, 139, 145, 151, 157, 163, 169, 175, 10, 22, 13, 11, 28, 104, 37, 57, 115, 46, 65, 129, 107, 75, 119, 110, 31, 43, 97, 78, 125, 58, 134, 140, 146, 152, 158, 164, 170, 176, 4, 19, 6, 8, 24, 44, 101, 94, 118, 130, 69, 71, 83, 34, 86, 124, 48, 106, 89, 40, 102, 91, 135, 141, 147, 153, 159, 165, 171, 177, 3, 20, 7, 17, 25, 87, 41, 120, 47, 80, 59, 62, 88, 45, 56, 131, 61, 126, 113, 92, 51, 98, 136, 142, 148, 154, 160, 166, 172, 178, 21, 18, 1, 26, 29, 39, 73, 121, 105, 77, 42, 114, 93, 82, 111, 109, 67, 79, 123, 64, 76, 33, 137, 143, 149, 155, 161, 167, 173, 179

FIG. 110 is a diagram that illustrates a 13th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 110, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179

FIG. 111 is a diagram that illustrates a 14th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 111, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179

FIG. 112 is a diagram that illustrates a 15th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 112, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

8, 112, 92, 165, 12, 55, 5, 126, 87, 70, 69, 94, 103, 78, 137, 148, 9, 60, 13, 7, 178, 79, 43, 136, 34, 68, 118, 152, 49, 15, 99, 61, 66, 28, 109, 125, 33, 167, 81, 93, 97, 26, 35, 30, 153, 131, 122, 71, 107, 130, 76, 4, 95, 42, 58, 134, 0, 89, 75, 40, 129, 31, 80, 101, 52, 16, 142, 44, 138, 46, 116, 27, 82, 88, 143, 128, 72, 29, 83, 117, 172, 14, 51, 159, 48, 160, 100, 1, 102, 90, 22, 3, 114, 19, 108, 113, 39, 73, 111, 155, 106, 105, 91, 150, 54, 25, 135, 139, 147, 36, 56, 123, 6, 67, 104, 96, 157, 10, 62, 164, 86, 74, 133, 120, 174, 53, 140, 156, 171, 149, 127, 85, 59, 124, 84, 11, 21, 132, 41, 145, 158, 32, 17, 23, 50, 169, 170, 38, 18, 151, 24, 166, 175, 2, 47, 57, 98, 20, 177, 161, 154, 176, 163, 37, 110, 168, 141, 64, 65, 173, 162, 121, 45, 77, 115, 179, 63, 119, 146, 144

FIG. 113 is a diagram that illustrates a 16th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 113, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

103, 138, 168, 82, 116, 45, 178, 28, 160, 2, 129, 148, 150, 23, 54, 106, 24, 78, 49, 87, 145, 179, 26, 112, 119, 12, 18, 174, 21, 48, 134, 137, 102, 147, 152, 72, 68, 3, 22, 169, 30, 64, 108, 142, 131, 13, 113, 115, 121, 37, 133, 136, 101, 59, 73, 161, 38, 164, 43, 167, 42, 144, 41, 85, 91, 58, 128, 154, 172, 57, 75, 17, 157, 19, 4, 86, 15, 25, 35, 9, 105, 123, 14, 34, 56, 111, 60, 90, 74, 149, 146, 62, 163, 31, 16, 141, 88, 6, 155, 130, 89, 107, 135, 79, 8, 10, 124, 171, 114, 162, 33, 66, 126, 71, 44, 158, 51, 84, 165, 173, 120, 7, 11, 170, 176, 1, 156, 96, 175, 153, 36, 47, 110, 63, 132, 29, 95, 143, 98, 70, 20, 122, 53, 100, 93, 140, 109, 139, 76, 151, 52, 61, 46, 125, 94, 50, 67, 81, 69, 65, 40, 127, 77, 32, 39, 27, 99, 97, 159, 166, 80, 117, 55, 92, 118, 0, 5, 83, 177, 104

FIG. 114 is a diagram that illustrates a 17th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 114, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

104, 120, 47, 136, 116, 109, 22, 20, 117, 61, 52, 108, 86, 99, 76, 90, 37, 58, 36, 138, 95, 130, 177, 93, 56, 33, 24, 82, 0, 67, 83, 46, 79, 70, 154, 18, 75, 43, 49, 63, 162, 16, 167, 80, 125, 1, 123, 107, 9, 45, 53, 15, 38, 23, 57, 141, 4, 178, 165, 113, 21, 105, 11, 124, 126, 77, 146, 29, 131, 27, 176, 40, 74, 91, 140, 64, 73, 44, 129, 157, 172, 51, 10, 128, 119, 163, 103, 28, 85, 156, 78, 6, 8, 173, 160, 106, 31, 54, 122, 25, 139, 68, 150, 164, 87, 135, 97, 166, 42, 169, 161, 137, 26, 39, 133, 5, 94, 69, 2, 30, 171, 149, 115, 96, 145, 101, 92, 143, 12, 88, 81, 71, 19, 147, 50, 152, 159, 155, 151, 174, 60, 32, 3, 142, 72, 14, 170, 112, 65, 89, 175, 158, 17, 114, 62, 144, 13, 98, 66, 59, 7, 118, 48, 153, 100, 134, 84, 111, 132, 127, 41, 168, 110, 102, 34, 121, 179, 148, 55,

FIG. 115 is a diagram that illustrates an 18th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 115, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

37, 98, 160, 63, 18, 6, 94, 136, 8, 50, 0, 75, 65, 32, 107, 60, 108, 17, 21, 156, 157, 5, 73, 66, 38, 177, 162, 130, 171, 76, 57, 126, 103, 62, 120, 134, 154, 101, 143, 29, 13, 149, 16, 33, 55, 56, 159, 128, 23, 146, 153, 141, 169, 49, 46, 152, 89, 155, 111, 127, 48, 14, 93, 41, 7, 78, 135, 69, 123, 179, 36, 87, 27, 58, 88, 170, 125, 110, 15, 97, 178, 90, 121, 173, 30, 102, 10, 80, 104, 166, 64, 4, 147, 1, 52, 45, 148, 68, 158, 31, 140, 100, 85, 115, 151, 70, 39, 82, 122, 79, 12, 91, 133, 132, 22, 163, 47, 19, 119, 144, 35, 25, 42, 83, 92, 26, 72, 138, 54, 124, 24, 74, 118, 117, 168, 71, 109, 112, 106, 176, 175, 44, 145, 11, 9, 161, 96, 77, 174, 137, 34, 84, 2, 164, 129, 43, 150, 61, 53, 20, 165, 113, 142, 116, 95, 3, 28, 40, 81, 99, 139, 114, 59, 67, 172, 131, 105, 167, 51, 86

FIG. 116 is a diagram that illustrates a 19th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 116, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

58, 70, 23, 32, 26, 63, 55, 48, 35, 41, 53, 20, 38, 51, 61, 65, 44, 29, 7, 2, 113, 68, 96, 104, 106, 89, 27, 0, 119, 21, 4, 49, 46, 100, 13, 36, 57, 98, 102, 9, 42, 39, 33, 62, 22, 95, 101, 15, 91, 25, 93, 132, 69, 87, 47, 59, 67, 124, 17, 11, 31, 43, 40, 37, 85, 50, 97, 140, 45, 92, 56, 30, 34, 60, 107, 24, 52, 94, 64, 5, 71, 90, 66, 103, 88, 86, 84, 19, 169, 159, 147, 126, 28, 130, 14, 162, 144, 166, 108, 153, 115, 135, 120, 122, 112, 139, 151, 156, 16, 172, 164, 123, 99, 54, 136, 81, 105, 128, 116, 150, 155, 76, 18, 142, 170, 175, 83, 146, 78, 109, 73, 131, 127, 82, 167, 77, 110, 79, 137, 152, 3, 173, 148, 72, 158, 117, 1, 6, 12, 8, 161, 74, 143, 133, 168, 171, 134, 163, 138, 121, 141, 160, 111, 10, 149, 80, 75, 165, 157, 174, 129, 145, 114, 125, 154, 118, 176, 177, 178, 179

FIG. 117 is a diagram that illustrates a 20th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 117, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

40, 159, 100, 14, 88, 75, 53, 24, 157, 84, 23, 77, 140, 145, 32, 28, 112, 39, 76, 50, 93, 27, 107, 25, 152, 101, 127, 5, 129, 71, 9, 21, 96, 73, 35, 106, 158, 49, 136, 30, 137, 115, 139, 48, 167, 85, 74, 72, 7, 110, 161, 41, 170, 147, 82, 128, 149, 33, 8, 120, 47, 68, 58, 67, 87, 155, 11, 18, 103, 151, 29, 36, 83, 135, 79, 150, 97, 54, 70, 138, 156, 31, 121, 34, 20, 130, 61, 57, 2, 166, 117, 15, 6, 165, 118, 98, 116, 131, 109, 62, 126, 175, 22, 111, 164, 16, 133, 102, 55, 105, 64, 177, 78, 37, 162, 124, 119, 19, 4, 69, 132, 65, 123, 160, 17, 52, 38, 1, 80, 90, 42, 81, 104, 13, 144, 51, 114, 3, 43, 146, 163, 59, 45, 89, 122, 169, 44, 94, 86, 99, 66, 171, 173, 0, 141, 148, 176, 26, 143, 178, 60, 153, 142, 91, 179, 12, 168, 113, 95, 174, 56, 134, 92, 46, 108, 125, 10, 172, 154, 63

FIG. 118 is a diagram that illustrates a 21st example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 118, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

143, 57, 67, 26, 134, 112, 136, 103, 13, 94, 16, 116, 169, 95, 98, 6, 174, 173, 102, 15, 114, 39, 127, 78, 18, 123, 121, 4, 89, 115, 24, 108, 74, 63, 175, 82, 48, 20, 104, 92, 27, 3, 33, 106, 62, 148, 154, 25, 129, 69, 178, 156, 87, 83, 100, 122, 70, 93, 50, 140, 43, 125, 166, 41, 128, 85, 157, 49, 86, 66, 79, 130, 133, 171, 21, 165, 126, 51, 153, 38, 142, 109, 10, 65, 23, 91, 90, 73, 61, 42, 47, 131, 77, 9, 58, 96, 101, 37, 7, 159, 44, 2, 170, 160, 162, 0, 137, 31, 45, 110, 144, 88, 8, 11, 40, 81, 168, 135, 56, 151, 107, 105, 32, 120, 132, 1, 84, 161, 179, 72, 176, 71, 145, 139, 75, 141, 97, 17, 149, 124, 80, 60, 36, 52, 164, 53, 158, 113, 34, 76, 5, 111, 155, 138, 19, 35, 167, 172, 14, 147, 55, 152, 59, 64, 54, 117, 146, 118, 119, 150, 29, 163, 68, 99, 46, 177, 28, 22, 30, 12

FIG. 119 is a diagram that illustrates a 22nd example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 119, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

116, 47, 155, 89, 109, 137, 103, 60, 114, 14, 148, 100, 28, 132, 129, 105, 154, 7, 167, 140, 160, 30, 57, 32, 81, 3, 86, 45, 69, 147, 125, 52, 20, 22, 156, 168, 17, 5, 93, 53, 61, 149, 56, 62, 112, 48, 11, 21, 166, 73, 158, 104, 79, 128, 135, 126, 63, 26, 44, 97, 13, 151, 123, 41, 118, 35, 131, 8, 90, 58, 134, 6, 78, 130, 82, 106, 99, 178, 102, 29, 108, 120, 107, 139, 23, 85, 36, 172, 174, 138, 95, 145, 170, 122, 50, 19, 91, 67, 101, 92, 179, 27, 94, 66, 171, 39, 68, 9, 59, 146, 15, 31, 38, 49, 37, 64, 77, 152, 144, 72, 165, 163, 24, 1, 2, 111, 80, 124, 43, 136, 127, 153, 75, 42, 113, 18, 164, 133, 142, 98, 96, 4, 51, 150, 46, 121, 76, 10, 25, 176, 34, 110, 115, 143, 173, 169, 40, 65, 157, 175, 70, 33, 141, 71, 119, 16, 162, 177, 12, 84, 87, 117, 0, 88, 161, 55, 54, 83, 74, 159

FIG. 120 is a diagram that illustrates a 23rd example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 120, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

62, 17, 10, 25, 174, 13, 159, 14, 108, 0, 42, 57, 78, 67, 41, 132, 110, 87, 77, 27, 88, 56, 8, 161, 7, 164, 171, 44, 75, 176, 145, 165, 157, 34, 142, 98, 103, 52, 11, 82, 141, 116, 15, 158, 139, 120, 36, 61, 20, 112, 144, 53, 128, 24, 96, 122, 114, 104, 150, 50, 51, 80, 109, 33, 5, 95, 59, 16, 134, 105, 111, 21, 40, 146, 18, 133, 60, 23, 160, 106, 32, 79, 55, 6, 1, 154, 117, 19, 152, 167, 166, 30, 35, 100, 74, 131, 99, 156, 39, 76, 86, 43, 178, 155, 179, 177, 136, 175, 81, 64, 124, 153, 84, 163, 135, 115, 125, 47, 45, 143, 72, 48, 172, 97, 85, 107, 126, 91, 129, 137, 83, 118, 54, 2, 9, 58, 169, 73, 123, 4, 92, 168, 162, 94, 138, 119, 22, 31, 63, 89, 90, 69, 49, 173, 28, 127, 26, 29, 101, 170, 93, 140, 147, 149, 148, 66, 65, 121, 12, 71, 37, 70, 102, 46, 38, 68, 130, 3, 113, 151

FIG. 121 is a diagram that illustrates a 24th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 121, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

168, 18, 46, 131, 88, 90, 11, 89, 111, 174, 172, 38, 78, 153, 9, 80, 53, 27, 44, 79, 35, 83, 171, 51, 37, 99, 95, 119, 117, 127, 112, 166, 28, 123, 33, 160, 29, 6, 135, 10, 66, 69, 74, 92, 15, 109, 106, 178, 65, 141, 0, 3, 154, 156, 164, 7, 45, 115, 122, 148, 110, 24, 121, 126, 23, 175, 21, 113, 58, 43, 26, 143, 56, 142, 39, 147, 30, 25, 101, 145, 136, 19, 4, 48, 158, 118, 133, 49, 20, 102, 14, 151, 5, 2, 72, 103, 75, 60, 84, 34, 157, 169, 31, 161, 81, 70, 85, 159, 132, 41, 152, 179, 98, 144, 36, 16, 87, 40, 91, 1, 130, 108, 139, 94, 97, 8, 104, 13, 150, 137, 47, 73, 62, 12, 50, 61, 105, 100, 86, 146, 165, 22, 17, 57, 167, 59, 96, 120, 155, 77, 162, 55, 68, 140, 134, 82, 76, 125, 32, 176, 138, 173, 177, 163, 107, 170, 71, 129, 63, 93, 42, 52, 116, 149, 54, 128, 124, 114, 67, 64

FIG. 122 is a diagram that illustrates a 25th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 122, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

18, 150, 165, 42, 81, 48, 63, 45, 93, 152, 25, 16, 174, 29, 47, 83, 8, 60, 30, 66, 11, 113, 44, 148, 4, 155, 59, 33, 134, 99, 32, 176, 109, 72, 36, 111, 106, 73, 170, 126, 64, 88, 20, 17, 172, 154, 120, 121, 139, 77, 98, 43, 105, 133, 19, 41, 78, 15, 7, 145, 94, 136, 131, 163, 65, 31, 96, 79, 119, 143, 10, 95, 9, 146, 14, 118, 162, 37, 97, 49, 22, 51, 127, 6, 71, 132, 87, 21, 39, 38, 54, 115, 159, 161, 84, 108, 13, 102, 135, 103, 156, 67, 173, 76, 75, 164, 52, 142, 69, 130, 56, 153, 74, 166, 158, 124, 141, 58, 116, 85, 175, 169, 168, 147, 35, 62, 5, 123, 100, 90, 122, 101, 149, 112, 140, 86, 68, 89, 125, 27, 177, 160, 0, 80, 55, 151, 53, 2, 70, 167, 114, 129, 179, 138, 1, 92, 26, 50, 28, 110, 61, 82, 91, 117, 107, 178, 34, 157, 137, 128, 40, 24, 57, 3, 171, 46, 104, 12, 144, 23

FIG. 123 is a diagram that illustrates a 26th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 123, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

18, 8, 166, 117, 4, 111, 142, 148, 176, 91, 120, 144, 99, 124, 20, 25, 31, 78, 36, 72, 2, 98, 93, 74, 174, 52, 152, 62, 88, 75, 23, 97, 147, 15, 71, 1, 127, 138, 81, 83, 68, 94, 112, 119, 121, 89, 163, 85, 86, 28, 17, 64, 14, 44, 158, 159, 150, 32, 128, 70, 90, 29, 30, 63, 100, 65, 129, 140, 177, 46, 84, 92, 10, 33, 58, 7, 96, 151, 171, 40, 76, 6, 3, 37, 104, 57, 135, 103, 141, 107, 116, 160, 41, 153, 175, 55, 130, 118, 131, 42, 27, 133, 95, 179, 34, 21, 87, 106, 105, 108, 79, 134, 113, 26, 164, 114, 73, 102, 77, 22, 110, 161, 43, 122, 123, 82, 5, 48, 139, 60, 49, 154, 115, 146, 67, 69, 137, 109, 143, 24, 101, 45, 16, 12, 19, 178, 80, 51, 47, 149, 50, 172, 170, 169, 61, 9, 39, 136, 59, 38, 54, 156, 126, 125, 145, 0, 13, 155, 132, 162, 11, 157, 66, 165, 173, 56, 168, 167, 53, 35

FIG. 124 is a diagram that illustrates a 27th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 124, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

77, 50, 109, 128, 153, 12, 48, 17, 147, 55, 173, 172, 135, 121, 99, 162, 52, 40, 129, 168, 103, 87, 134, 105, 179, 10, 131, 151, 3, 26, 100, 15, 123, 88, 18, 91, 54, 160, 49, 1, 76, 80, 74, 31, 47, 58, 161, 9, 16, 34, 41, 21, 177, 11, 63, 6, 39, 165, 169, 125, 114, 57, 37, 67, 93, 96, 73, 106, 83, 166, 24, 51, 142, 65, 43, 64, 53, 72, 156, 81, 4, 155, 33, 163, 56, 150, 70, 167, 107, 112, 144, 149, 36, 32, 35, 59, 101, 29, 127, 138, 176, 90, 141, 92, 170, 102, 119, 25, 75, 14, 0, 68, 20, 97, 110, 28, 89, 118, 154, 126, 2, 22, 124, 85, 175, 78, 46, 152, 23, 86, 27, 79, 130, 66, 45, 113, 111, 62, 61, 7, 30, 133, 108, 171, 143, 60, 178, 5, 122, 44, 38, 148, 157, 84, 42, 139, 145, 8, 104, 115, 71, 137, 132, 146, 164, 98, 13, 117, 174, 158, 95, 116, 140, 94, 136, 120, 82, 69, 159, 19

FIG. 125 is a diagram that illustrates a 28th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 125, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

51, 47, 53, 43, 55, 59, 49, 33, 35, 31, 24, 37, 0, 2, 45, 41, 39, 57, 42, 44, 52, 40, 23, 30, 32, 34, 54, 56, 46, 50, 122, 48, 1, 36, 38, 58, 77, 3, 65, 81, 67, 147, 83, 69, 26, 75, 85, 73, 79, 145, 71, 63, 5, 61, 70, 78, 68, 62, 66, 6, 64, 149, 60, 82, 80, 4, 76, 84, 72, 154, 86, 74, 89, 128, 137, 91, 141, 93, 101, 7, 87, 9, 103, 99, 95, 11, 13, 143, 97, 133, 136, 12, 100, 94, 14, 88, 142, 96, 92, 8, 152, 10, 139, 102, 104, 132, 90, 98, 114, 112, 146, 123, 110, 15, 125, 150, 120, 153, 29, 106, 134, 27, 127, 108, 130, 116, 28, 107, 126, 25, 131, 124, 129, 151, 121, 105, 111, 115, 135, 148, 109, 117, 158, 113, 170, 119, 162, 178, 155, 176, 18, 20, 164, 157, 160, 22, 140, 16, 168, 166, 172, 174, 175, 179, 118, 138, 156, 19, 169, 167, 163, 173, 161, 177, 165, 144, 171, 17, 21, 159

FIG. 126 is a diagram that illustrates a 29th example of the GW pattern for an LDPC code of which the code length N is 64 kbits.

According to the GW pattern illustrated in FIG. 126, a sequence of bit groups 0 to 179 of the LDPC code of 64 kbits is interleaved into a sequence of the following bit groups.

49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, 175

The first to 29th examples of the GW pattern for the LDPC code of which the code length N is 64 kbits can be applied to any combination of the LDPC code having a code length N of 64 kbits and an arbitrary coding rate r and an arbitrary modulation scheme (constellation).

However, in the group-wise interleave, by setting the GW pattern to be applied to each combination of the code length N of the LDPC code, the coding rate r of the LDPC code, and the modulation scheme (constellation), the error rate of each combination can be further improved.

By applying the GW pattern illustrated in FIG. 98, for example, to the combination of the ETRI code of (64 k, 5/15) and the QPSK, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 99, for example, to the combination of the ETRI code of (64 k, 5/15) and the 16 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 100, for example, to the combination of the ETRI code of (64 k, 5/15) and the 64 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 101, for example, to the combination of the Sony code of (64 k, 7/15) and the QPSK, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 102, for example, to the combination of the Sony code of (64 k, 7/15) and the 16 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 103, for example, to the combination of the Sony code of (64 k, 7/15) and the 64 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 104, for example, to the combination of the Sony code of (64 k, 9/15) and the QPSK, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 105, for example, to the combination of the Sony code of (64 k, 9/15) and the 16 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 106, for example, to the combination of the Sony code of (64 k, 9/15) and the 64 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 107, for example, to the combination of the Sony code of (64 k, 11/15) and the QPSK, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 108, for example, to the combination of the Sony code of (64 k, 11/15) and the 16 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 109, for example, to the combination of the Sony code of (64 k, 11/15) and the 64 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 110, for example, to the combination of the Sony code of (64 k, 13/15) and the QPSK, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 111, for example, to the combination of the Sony code of (64 k, 13/15) and the 16 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 112, for example, to the combination of the Sony code of (64 k, 13/15) and the 64 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 113, for example, to the combination of the ETRI code of (64 k, 5/15) and the 256 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 114, for example, to the combination of the ETRI code of (64 k, 7/15) and the 256 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 115, for example, to the combination of the Sony code of (64 k, 7/15) and the 256 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 116, for example, to the combination of the Sony code of (64 k, 9/15) and the 256 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 117, for example, to the combination of the NERC code of (64 k, 9/15) and the 256 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 118, for example, to the combination of the Sony code of (64 k, 11/15) and the 256 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 119, for example, to the combination of the Sony code of (64 k, 13/15) and the 256 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 120, for example, to the combination of the ETRI code of (64 k, 5/15) and the 1024 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 121, for example, to the combination of the ETRI code of (64 k, 7/15) and the 1024 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 122, for example, to the combination of the Sony code of (64 k, 7/15) and the 1024 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 123, for example, to the combination of the Sony code of (64 k, 9/15) and the 1024 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 124, for example, to the combination of the NERC code of (64 k, 9/15) and the 1024 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 125, for example, to the combination of the Sony code of (64 k, 11/15) and the 1024 QAM, particularly, an excellent error rate can be achieved.

By applying the GW pattern illustrated in FIG. 126, for example, to the combination of the Sony code of (64 k, 13/15) and the 1024 QAM, particularly, an excellent error rate can be achieved.

FIG. 127 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 98 is applied to a combination of the ETRI code of (64 k, 5/15) and the QPSK.

FIG. 128 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 99 is applied to a combination of the ETRI code of (64 k, 5/15) and the 16 QAM.

FIG. 129 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 100 is applied to a combination of the ETRI code of (64 k, 5/15) and the 64 QAM.

FIG. 130 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 101 is applied to a combination of the Sony code of (64 k, 7/15) and the QPSK.

FIG. 131 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 102 is applied to a combination of the Sony code of (64 k, 7/15) and the 16 QAM.

FIG. 132 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 103 is applied to a combination of the Sony code of (64 k, 7/15) and the 64 QAM.

FIG. 133 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 104 is applied to a combination of the Sony code of (64 k, 9/15) and the QPSK.

FIG. 134 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 105 is applied to a combination of the Sony code of (64 k, 9/15) and the 16 QAM.

FIG. 135 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 106 is applied to a combination of the Sony code of (64 k, 9/15) and the 64 QAM.

FIG. 136 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 107 is applied to a combination of the Sony code of (64 k, 11/15) and the QPSK.

FIG. 137 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 108 is applied to a combination of the Sony code of (64 k, 11/15) and the 16 QAM.

FIG. 138 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 109 is applied to a combination of the Sony code of (64 k, 11/15) and the 64 QAM.

FIG. 139 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 110 is applied to a combination of the Sony code of (64 k, 13/15) and the QPSK.

FIG. 140 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 111 is applied to a combination of the Sony code of (64 k, 13/15) and the 16 QAM.

FIG. 141 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 112 is applied to a combination of the Sony code of (64 k, 13/15) and the 64 QAM.

FIG. 142 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 113 is applied to a combination of the ETRI code of (64 k, 5/15) and the 256 QAM.

FIG. 143 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 114 is applied to a combination of the ETRI code of (64 k, 7/15) and the 256 QAM.

FIG. 144 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 115 is applied to a combination of the Sony code of (64 k, 7/15) and the 256 QAM.

FIG. 145 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 116 is applied to a combination of the Sony code of (64 k, 9/15) and the 256 QAM.

FIG. 146 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 117 is applied to a combination of the NERC code of (64 k, 9/15) and the 256 QAM.

FIG. 147 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 118 is applied to a combination of the Sony code of (64 k, 11/15) and the 256 QAM.

FIG. 148 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 119 is applied to a combination of the Sony code of (64 k, 13/15) and the 256 QAM.

FIG. 149 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 120 is applied to a combination of the ETRI code of (64 k, 5/15) and the 1024 QAM.

FIG. 150 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 121 is applied to a combination of the ETRI code of (64 k, 7/15) and the 1024 QAM.

FIG. 151 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 122 is applied to a combination of the Sony code of (64 k, 7/15) and the 1024 QAM.

FIG. 152 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 123 is applied to a combination of the Sony code of (64 k, 9/15) and the 1024 QAM.

FIG. 153 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 124 is applied to a combination of the NERC code of (64 k, 9/15) and the 1024 QAM.

FIG. 154 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 125 is applied to a combination of the Sony code of (64 k, 11/15) and the 1024 QAM.

FIG. 155 is a diagram that illustrates a BER/FER curve as a simulation result of a simulation of measuring an error rate in a case where the GW pattern illustrated in FIG. 126 is applied to a combination of the Sony code of (64 k, 13/15) and the 1024 QAM.

Note that FIGS. 127 to 155 illustrate BER/FER curves in a case where an AWGN channel is employed as the communication line 13 (FIG. 7) (upper drawings) and BER/FER curves in a case where a Rayleigh (fading) channel is employed as the communication line 13 (FIG. 7) (lower drawings).

In addition, in FIGS. 127 to 155, each solid line (w bil) represents a BER/FER curve in a case where the parity interleave, the group-wise interleave, and the block-wise interleave are performed, and each dotted line (w/o bil) represents a BER/FER curve in a case where the parity interleave, the group-wise interleave, and the block-wise interleave are not performed.

As illustrated in FIGS. 127 to 155, in a case where the parity interleave, the group-wise interleave, and the block-wise interleave are performed, it can be checked that the BER/FER is improved, and an excellent error rate can be achieved, compared to a case where such interleave is not performed.

Note that the GW patterns illustrated in FIGS. 98 to 126 also can be applied to a constellation in which the signal point arrangements illustrated in FIGS. 87 to 93 are symmetrically moved with respect to the I axis or the Q axis, a constellation in which the signal point arrangements described above are symmetrically moved with respect to the origin, a constellation in which the signal point arrangements described above are rotated with the origin used at its center by an arbitrary angle, and the like in addition to the constellation of QPSK, 16 QAM, 64 QAM, 256 QAM, and 1024 QAM of the signal point arrangements illustrated in FIGS. 87 to 93 described above, and effects similar to those of case where the GW patterns illustrated in FIGS. 87 to 93 are applied to the constellation of QPSK, 16 QAM, 64 QAM, 256 QAM, and 1024 QAM of the signal point arrangements illustrated in FIGS. 87 to 93 can be acquired.

Furthermore, the GW pattern illustrated in FIGS. 98 to 126 also can be applied to a constellation in which the most significant bit (MSB) and the least significant bit (LSB) of the symbol to be associated with (allocated to) the signal point are interchanged in the signal point arrangements illustrated in FIGS. 87 to 93 in addition to the constellations of QPSK, 16 QAM, 64 QAM, 256 QAM, and 1024 QAM of the signal point arrangements illustrated in FIGS. 87 to 93, and effects similar to those of case where the GW patterns illustrated in FIGS. 87 to 93 are applied to the constellations of QPSK, 16 QAM, 64 QAM, 256 QAM, and 1024 QAM of the signal point arrangements illustrated in FIGS. 87 to 93 can be acquired.

<Configuration Example of Receiving Device 12>

FIG. 156 is a block diagram illustrating a configuration example of the receiving device 12 illustrated in FIG. 7.

An OFDM processing unit (OFDM operation) 151 receives an OFDM signal from the transmitting device 11 (FIG. 7) and performs signal processing of the OFDM signal. Data that is acquired by performing the signal processing performed by the OFDM processing unit 151 is supplied to a frame managing unit (Frame Management) 152.

The frame managing unit 152 performs processing (frame interpretation) of a frame configured by the data supplied from the OFDM processing unit 151 and respectively supplies a signal of target data acquired as a result thereof and a signal of control data to frequency deinterleavers 161 and 153.

The frequency deinterleaver 153 performs frequency deinterleave in units of symbols for the data supplied from the frame managing unit 152 and supplies resultant data to a demapper 154.

The demapper 154 performs demapping (signal point arrangement decoding) and quadrature demodulation for the data (the data on the constellation) supplied from the frequency deinterleaver 153 on the basis of the arrangement (constellation) of the signal points determined according to the quadrature modulation performed on the transmitting device 11 side and supplies the data ((the likelihood of) the LDPC code) acquired as a result thereof to the LDPC decoder 155.

The LDPC decoder 155 performs LDPC decoding of the LDPC code supplied from the demapper 154 and supplies LDPC target data (in this case, a BCH code) acquired as a result thereof to a BCH decoder 156.

The BCH decoder 156 performs BCH decoding of the LDPC target data supplied from the LDPC decoder 155 and outputs control data (signaling) acquired as a result thereof.

Meanwhile, the frequency deinterleaver 161 performs frequency deinterleave in units of symbols for the data supplied from the frame managing unit 152 and supplies resultant data to a SISO/MISO decoder 162.

The SISO/MISO decoder 162 performs time-space decoding of the data supplied from the frequency deinterleaver 161 and supplies resultant data to a time deinterleaver 163.

The time deinterleaver 163 performs time deinterleave in units of symbols for the data supplied from the SISO/MISO decoder 162 and supplies resultant data to a demapper 164.

The demapper 164 performs demapping (signal point arrangement decoding) and quadrature demodulation for the data (the data on the constellation) supplied from the time deinterleaver 163 on the basis of the arrangement (constellation) of the signal points determined according to the quadrature modulation performed on the transmitting device 11 side and supplies the data acquired as a result thereof to a bit deinterleaver 165.

The bit deinterleaver 165 performs the bit deinterleave for the data supplied from the demapper 164 and supplies (the likelihood of) the LDPC code that is data after the bit deinterleave to an LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding of the LDPC code supplied from the bit deinterleaver 165 and supplies LDPC target data (here, a BCH code) acquired as a result thereof to a BCH decoder 167.

The BCH decoder 167 performs BCH decoding of the LDPC target data supplied from the LDPC decoder 155 and supplies data acquired as a result thereof to a BB descrambler 168.

The BB descrambler 168 performs BB descramble for the data supplied from the BCH decoder 167 and supplies data acquired as a result thereof to a null deletion unit 169.

The null deletion unit 169 deletes null inserted by the padder 112 illustrated in FIG. 8 from the data supplied from the BB descrambler 168 and supplies resultant data to a demultiplexer 170.

The demultiplexer 170 separates one or more streams (target data) multiplexed in the data supplied from the null deletion unit 169, performs necessary processing for the streams, and outputs processed streams as output streams.

Note that the receiving device 12 may be configured without arranging some of the blocks illustrated in FIG. 156. In other words, for example, in a case where the transmitting device 11 (FIG. 8) is configured without arranging the time interleaver 118, the SISO/MISO encoder 119, the frequency interleaver 120 and the frequency interleaver 124, the receiving device 12 may be configured without arranging the time deinterleaver 163, the SISO/MISO decoder 162, the frequency deinterleaver 161, and the frequency deinterleaver 153 that are blocks respectively corresponding to the time interleaver 118, the SISO/MISO encoder 119, the frequency interleaver 120, and the frequency interleaver 124 of the transmitting device 11.

<Configuration Example of Bit Deinterleaver 165>

FIG. 157 is a block diagram that illustrates a configuration example of the bit deinterleaver 165 illustrated in FIG. 156.

The bit deinterleaver 165 is configured with a block deinterleaver 54 and a group-wise deinterleaver 55 and performs the (bit) deinterleave of the symbol bits of the symbol that is the data supplied from the demapper 164 (FIG. 156).

In other words, the block deinterleaver 54 performs block deinterleave (the inverse process of the block interleave) corresponding to the block interleave performed by the block interleaver 25 illustrated in FIG. 9, in other words, the block deinterleave restoring the positions of (the likelihood of) of the code bits of the LDPC code rearranged by the block interleave to the original positions for the symbol bits of the symbol supplied from the demapper 164 as a target and supplies the LDPC code acquired as a result thereof to the group-wise deinterleaver 55.

The group-wise deinterleaver 55 performs group-wise deinterleave (the inverse process of the group-wise interleave) corresponding to the group-wise interleave performed by the group-wise interleaver 24 illustrated in FIG. 9, in other words, group-wise deinterleave for restoring the original sequence by rearranging the code bits of the LDPC code of which the sequence has been changed in units of bit groups by the group-wise interleave described above, for example, with reference to FIG. 97 in units of bit groups for the LDPC code supplied from the block deinterleaver 54 as a target.

Here, in a case where the parity interleave, the group-wise interleave, and the block interleave are performed for the LDPC code supplied from the demapper 164 to the bit deinterleaver 165, the bit deinterleaver 165 can perform all of the parity deinterleave (the inverse process of the parity interleave, in other words, the parity deinterleave for restoring the code bits of the LDPC code of which the sequence has been changed by the parity interleave to the original sequence) corresponding to the parity interleave, the block deinterleave corresponding to the block interleave, and the group-wise deinterleave corresponding to the group-wise interleave.

However, in the bit deinterleaver 165 illustrated in FIG. 157, while the block deinterleaver 54 that performs the block deinterleave corresponding to the block interleave and the group-wise deinterleaver 55 that performs the group-wise deinterleave corresponding to the group-wise interleave are arranged, the block that performs the parity deinterleave corresponding to the parity interleave is not arranged, and the parity deinterleave is not performed.

Accordingly, the LDPC code for which the block deinterleave and the group-wise deinterleave have been performed, but the parity deinterleave has not been performed is supplied from the bit deinterleaver 165 (the group-wise deinterleaver 55 thereof) to the LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding of the LDPC code supplied from the bit deinterleaver 165 by using the transformed parity check matrix (or the transformed parity check matrix (FIG. 29) acquired by performing row permutation for the parity check matrix (FIG. 27) of the ETRI type) acquired by performing at least the column permutation corresponding to the parity interleave for the parity check matrix H of the DVB type used for the LDPC coding by the LDPC encoder 115 illustrated in FIG. 8 and outputs data acquired as a result thereof as a decoding result of the LDPC target data.

FIG. 158 is a flowchart that illustrates a process performed by the demapper 164, the bit deinterleaver 165, and the LDPC decoder 166 illustrated in FIG. 157.

In step S111, the demapper 164 performs demapping and quadrature demodulation for the data (the data on the constellation mapped into the signal points) supplied from the time deinterleaver 163, and supplies resultant data to the bit deinterleaver 165, and the process proceeds to step S112

In step S112, the bit deinterleaver 165 performs the deinterleave (the bit deinterleave) for the data supplied from the demapper 164, and the process proceeds to step S113.

In other words, in step S112, in the bit deinterleaver 165, the block deinterleaver 54 performs block deinterleave for the data (symbol) supplied from the demapper 164 as a target and supplies the code bits of the LDPC code acquired as a result thereof to the group-wise deinterleaver 55.

The group-wise deinterleaver 55 performs group-wise deinterleave for the LDPC code supplied from the block deinterleaver 54 as a target and supplies (the likelihood of) the LDPC code acquired as a result thereof to the LDPC decoder 166.

In step S113, the LDPC decoder 166 performs LDPC decoding of the LDPC code supplied from the group-wise deinterleaver 55 by using the parity check matrix H used for the LDPC coding by the LDPC encoder 115 illustrated in FIG. 8, in other words, for example, by using the transformed parity check matrix acquired from the parity check matrix H and outputs the data acquired as a result thereof to the BCH decoder 167 as a decoding result of the LDPC target data.

Note that, in FIG. 157, similarly to the case illustrated in FIG. 9, for the convenience of description, while the block deinterleaver 54 that performs the block deinterleave and the group-wise deinterleaver 55 that performs the group-wise deinterleave are separately configured, the block deinterleaver 54 and the group-wise deinterleaver 55 may be integrally configured.

<LDPC Decoding>

The LDPC decoding performed by the LDPC decoder 166 illustrated in FIG. 156 will be further described.

As described above, the LDPC decoder 166 illustrated in FIG. 156 performs the LDPC decoding of the LDPC code, for which the block deinterleave and the group-wise deinterleave have been performed, but the parity deinterleave has not been performed, supplied from the group-wise deinterleaver 55 by using the transformed parity check matrix acquired by performing at least the column permutation corresponding to the parity interleave (or the transformed parity check matrix (FIG. 29) acquired by performing the row permutation for the parity check matrix of the ETRI type (FIG. 27)) for the parity check matrix H of the DVB type used for the LDPC coding by the LDPC encoder 115 illustrated in FIG. 8.

Here, LDPC decoding that can suppress an operation frequency to be in a sufficiently realizable range while suppressing the circuit scale by performing the LDPC decoding using the transformed parity check matrix has been proposed in advance (for example, see U.S. Pat. No. 4,224,777).

Thus, first, the LDPC decoding, which has been proposed in advance, using the transformed parity check matrix will be described with reference to FIGS. 159 to 162.

FIG. 159 illustrates an example of a parity check matrix H of an LDPC code having a code length N of 90 and a coding rate of 2/3.

Note that, in FIG. 159 (and FIGS. 160 and 161 to be described later), 0 is represented by a period (.).

In the parity check matrix H illustrated in FIG. 159, the parity matrix has a staircase structure.

FIG. 160 illustrates a parity check matrix H′ that is acquired by performing row permutation represented in Equation (11) and column permutation represented in Equation (12) for the parity check matrix H illustrated in FIG. 159. Row permutation: (6s+t+1)-th row→(5t+s+1)-th row   (11) Column permutation: (6x+y+61)-th column→(5y+x+61)-th column  (12)

In Equations (11) and (12), s, t, x, and y are integers respectively in the ranges of 0≤s<5, 0≤t<6, 0≤x<5, and 0≤t<6.

According to the row permutation represented in Equation (11), permutation is performed such that the 1st, 7th, 13th, 19th, and 25th rows having a remainder of 1 acquired when being divided by 6 are respectively replaced with the 1st, 2nd, 3rd, 4th, and 5th rows, and the 2nd, 8th, 14th, 20th, and 26th rows having a remainder of 2 acquired when being divided by 6 are respectively replaced with the 6th, 7th, 8th, 9th, and 10th rows.

In addition, according to the column permutation represented in Equation (12), permutation is performed such that the 61st, 67th, 73rd, 79th, and 85th columns having a remainder of 1 acquired when being divided by 6 are respectively replaced with the 61st, 62nd, 63rd, 64th, and 65th columns, and the 62nd, 68th, 74th, 80th, and 86th columns having a remainder of 2 acquired when being divided by 6 are respectively replaced with the 66th, 67th, 68th, 69th, and 70th columns for the 61st and following columns (parity matrix).

In this way, a matrix that is acquired by performing the permutation of the rows and the columns for the parity check matrix H illustrated in FIG. 159 is a parity check matrix H′ illustrated in FIG. 160.

In this case, even when the row permutation of the parity check matrix H is performed, the sequence of the code bits of the LDPC code is not influenced.

In addition, the column permutation represented in Equation (12) corresponds to the above-described parity interleave for interleaving the (K+qx+y+1)-th code bit into the position of the (K+Py+x+1)-th code bit when the information length K is 60, the unit size P is 5, and the divisor q (=M/P) of the parity length M (here, 30) is 6.

Accordingly, the parity check matrix H′ illustrated in FIG. 160 is a transformed parity check matrix acquired by performing at least column permutation replacing the (K+qx+y+1)-th column of the parity check matrix H illustrated in FIG. 159 (hereinafter, referred to as an original parity check matrix as is appropriate) with the (K+Py+x+1)-th column.

When the parity check matrix H′ illustrated in FIG. 160 is multiplied by a result acquired by performing the same permutation as Equation (12) for the LDPC code of the parity check matrix H illustrated in FIG. 159, a zero vector is output. In other words, when a row vector acquired by performing the column permutation represented in Equation (12) for a row vector c as the LDPC code (one code word) of the original parity check matrix H is represented as c′, Hc^(T) becomes the zero vector on the basis of the property of the parity check matrix. Accordingly, it is apparent that H′c′^(T) becomes the zero vector.

Accordingly, the transformed parity check matrix H′ illustrated in FIG. 160 is a parity check matrix of the LDPC code c′ that is acquired by performing the column permutation represented in Equation (12) for the LDPC code c of the original parity check matrix H.

Therefore, by performing the column permutation represented in Equation (12) for the LDPC code c of the original parity check matrix H, decoding the LDPC code c′ after the column permutation (LDPC decoding) using the transformed parity check matrix H′ illustrated in FIG. 160, and performing reverse permutation of the column permutation represented in Equation (12) for a result of the decoding, a decoding result similar to that in a case where the LDPC code of the original parity check matrix H is decoded using the parity check matrix H can be acquired.

FIG. 161 is a diagram that illustrates the transformed parity check matrix H′ illustrated in FIG. 160 with being spaced in units of 5×5 matrixes.

In FIG. 161, the transformed parity check matrix H′ is represented by a combination of a 5×5 (=P×P) unit matrix that has a unit size P, a matrix (hereinafter, appropriately referred to as a quasi unit matrix) acquired by setting one or more “1”s of the unit matrix to zero, a matrix (hereinafter, appropriately referred to as a shifted matrix) acquired by cyclically shifting the unit matrix or the quasi unit matrix, a sum (hereinafter, appropriately referred to as a sum matrix) of two or more matrixes of the unit matrix, the quasi unit matrix, and the shifted matrix, and a 5×5 zero matrix.

The transformed parity check matrix H′ illustrated in FIG. 161 can be regarded as being configured using the 5×5 unit matrix, the quasi unit matrix, the shifted matrix, the sum matrix, and the zero matrix. Therefore, hereinafter, the 5×5 matrixes (the unit matrix, the quasi unit matrix, the shifted matrix, the sum matrix, and the zero matrix) that constitute the transformed parity check matrix H′ will be appropriately referred to as constitutive matrixes.

For decoding the LDPC code of the parity check matrix represented by the P×P constitutive matrixes, an architecture in which P check node operations and variable node operations are simultaneously performed can be used.

FIG. 162 is a block diagram that illustrates a configuration example of a decoding device that performs such decoding.

In other words, FIG. 162 illustrates the configuration example of the decoding device that performs decoding of the LDPC code by using the transformed parity check matrix H′ illustrated in FIG. 161 acquired by performing at least the column permutation represented in Equation (12) for the original parity check matrix H illustrated in FIG. 159.

The decoding device illustrated in FIG. 162 includes a branch data storing memory 300 that includes 6 FIFOs 300 ₁ to 300 ₆, a selector 301 that selects the FIFOs 300 ₁ to 300 ₆, a check node calculating unit 302, two cyclic shift circuits 303 and 308, a branch data storing memory 304 that includes 18 FIFOs 304 ₁ to 304 ₁₈, a selector 305 that selects the FIFOs 304 ₁ to 304 ₁₈, a reception data memory 306 that stores reception data, a variable node calculating unit 307, a decoding word calculating unit 309, a reception data rearranging unit 310, and a decoded data rearranging unit 311.

First, a method of storing data in the branch data storing memories 300 and 304 will be described.

The branch data storing memory 300 includes the 6 FIFOs 300 ₁ to 300 ₆ that correspond to a number acquired by dividing the number “30” of rows of the transformed parity check matrix H′ illustrated in FIG. 161 by the number “5” of rows (the unit size P) of the constitutive matrix. The FIFO 300 _(y) (y=1, 2, . . . , 6) includes a plurality of stages of storage areas. For the storage area of each stage, messages corresponding to five branches that correspond to the number of rows and the number of columns (the unit size P) of the constitutive matrix can be simultaneously read or written. The number of stages of the storage areas of the FIFO 300 _(y) is 9 that is a maximum number of the number (Hamming weight) of “1” of the transformed parity check matrix illustrated in FIG. 161 in the row direction.

In the FIFO 300 ₁, data (messages v_(i) from variable nodes) corresponding to positions of “1”s in the first to fifth rows of the transformed parity check matrix H′ illustrated in FIG. 161 is stored in the form of filling each row in a horizontal direction (a form in which “0” is ignored). In other words, when a j-th row and an i-th column are represented as (j, i), data corresponding to positions of “1”s in a 5×5 unit matrix of (1, 1) to (5, 5) of the transformed parity check matrix H′ is stored in the storage area of the first stage of the FIFO 300 ₁. In the storage area of the second stage, data corresponding to positions of “1” in a shifted matrix (shifted matrix acquired by cyclically shifting the 5×5 unit matrix to the right side by 3) of (1, 21) to (5, 25) of the transformed parity check matrix H′ is stored. Similarly, in the storage areas of the third to eighth stages, data is stored in association with the transformed parity check matrix H′. In the storage area of the ninth stage, data corresponding to the positions of “1”s in a shifted matrix (a shifted matrix acquired by replacing “1” included in the first row of the 5×5 unit matrix with “0” and cyclically shifting the unit matrix to the left side by 1) of (1, 86) to (5, 90) of the transformed parity check matrix H′ is stored.

In the FIFO 300 ₂, data corresponding to the positions of “1”s in the sixth to tenth rows of the transformed parity check matrix H′ illustrated in FIG. 161 is stored. In other words, in the storage area of the first stage of the FIFO 300 ₂, data corresponding to the positions of “1”s in a first shifted matrix constituting a sum matrix (a sum matrix that is a sum of the first shifted matrix acquired by cyclically shifting the 5×5 unit matrix to the right side by one and a second shifted matrix acquired by cyclically shifting the 5×5 unit matrix to the right side by two) of (6, 1) to (10, 5) of the transformed parity check matrix H′ is stored. In addition, in the storage area of the second stage, data corresponding to the positions of “1”s in the second shifted matrix constituting the sum matrix of (6, 1) to (10, 5) of the transformed parity check matrix H′ is stored.

In other words, for a constitutive matrix of which the weight is two or more, when the constitutive matrix is represented by a sum of a plurality of a P×P unit matrix of which the weight is 1, a quasi unit matrix acquired by setting one or more elements of “1”s in the unit matrix to “0”, and a shifted matrix acquired by cyclically shifting the unit matrix or the quasi unit matrix, data (messages corresponding to branches belonging to the unit matrix, the quasi unit matrix, or the shifted matrix) corresponding to the positions of “1”s in the unit matrix of the weight of 1, the quasi unit matrix, or the shifted matrix is stored at the same address (the same FIFO among the FIFOs 300 ₁ to 300 ₆).

Subsequently, also in the storage areas of the third to ninth stages, data is stored in association with the transformed parity check matrix H′.

Also in the FIFOs 300 ₃ to 300 ₆, data is similarly stored in association with the transformed parity check matrix H′.

The branch data storing memory 304 includes 18 FIFOs 304 ₁ to 304 ₁₈ that correspond to a number acquired by dividing the number “90” of columns of the transformed parity check matrix H′ by 5 that is the number of columns (the unit size P) of the constitutive matrix. The FIFO 304 _(x) (here, x=1, 2, . . . , 18) includes a plurality of stages of storage areas. For the storage area of each stage, messages corresponding to five branches corresponding to the number of rows and the number of columns (the unit size P) of the constitutive matrix can be simultaneously read or written.

In the FIFO 304 ₁, data (messages u_(j) from check nodes) corresponding to the positions of “1”s in the first to fifth columns of the transformed parity check matrix H′ illustrated in FIG. 161 is stored in the form of filling each column in the vertical direction (a form in which “0” is ignored). In other words, data corresponding to the positions of “1”s in the 5×5 unit matrix of (1, 1) to (5, 5) of the transformed parity check matrix H′ is stored in the storage area of the first stage of the FIFO 304 ₁. In the storage area of the second stage, data corresponding to the positions of “1”s in the first shifted matrix constituting a sum matrix (a sum matrix that is a sum of the first shifted matrix acquired by cyclically shifting the 5×5 unit matrix to the right side by one and the second shifted matrix acquired by cyclically shifting the 5×5 unit matrix to the right side by two) of (6, 1) to (10, 5) of the transformed parity check matrix H′ is stored. In addition, in the storage area of the third stage, data corresponding to the positions of “1” in the second shifted matrix constituting the sum matrix of (6, 1) to (10, 5) of the transformed parity check matrix H′ is stored.

In other words, for a constitutive matrix of which the weight is two or more, when the constitutive matrix is represented by a sum of a plurality of a P×P unit matrix of which the weight is 1, a quasi unit matrix acquired by setting one or more elements of “1”s in the unit matrix to “0”, and a shifted matrix acquired by cyclically shifting the unit matrix or the quasi unit matrix, data (messages corresponding to branches belonging to the unit matrix, the quasi unit matrix, or the shifted matrix) corresponding to the positions of “1”s in the unit matrix having a weight of 1, the quasi unit matrix, or the shifted matrix is stored at the same address (the same FIFO among the FIFOs 304 ₁ to 304 ₁₈).

Subsequently, also in the storage areas of the fourth and fifth stages, data is stored in association with the transformed parity check matrix H′ The number of stages of the storage areas of the FIFO 304 ₁ is 5 that is a maximum number of the number (Hamming weight) of “1”s in the row direction in the first to fifth columns of the transformed parity check matrix H′.

Similarly, in the FIFOs 304 ₂ and 304 ₃, data is stored in association with the transformed parity check matrix H′, and each length (the number of stages) is 5. Similarly, in the FIFOs 304 ₄ to 304 ₁₂, data is stored in association with the transformed parity check matrix H′, and each length is 3. Similarly, in the FIFOs 304 ₁₃ to 304 ₁₈, data is stored in association with the transformed parity check matrix H′, and each length is 2.

Next, an operation of the decoding device illustrated in FIG. 162 will be described.

The branch data storing memory 300 includes the 6 FIFOs 300 ₁ to 300 ₆ and, according to information (matrix data) D312 representing rows of the transformed parity check matrix H′ illustrated in FIG. 161 to which five messages D311 supplied from a cyclic shift circuit 308 of a previous stage belongs, selects a FIFO storing data from among the FIFOs 300 ₁ to 300 ₆ and sequentially stores the five messages D311 collectively in the selected FIFO. In order to read the data, the branch data storing memory 300 sequentially reads the five messages D300 ₁ from the FIFO 300 ₁ and supplies the read messages to the selector 301 of a next stage. After reading of the messages from the FIFO 300 ₁ ends, the branch data storing memory 300 sequentially reads messages also from the FIFOs 300 ₂ to 300 ₆ and supplies the read messages to the selector 301.

The selector 301 selects the five messages supplied from the FIFO from which data is currently read from among the FIFOs 300 ₁ to 300 ₆, according to a select signal D301, and supplies the selected messages as messages D302 to the check node calculating unit 302.

The check node calculating unit 302 includes five check node calculators 302 ₁ to 302 ₅, performs a check node operation according to Equation (7) by using the messages D302 (D302 ₁ to D302 ₅) (messages v₁ represented in Equation (7)) supplied through the selector 301, and supplies five messages D303 (D303 ₁ to D303 ₅) (messages u_(j) of Equation (7)) acquired as a result of the check node operation to a cyclic shift circuit 303.

The cyclic shift circuit 303 cyclically shifts the five messages D303 ₁ to D303 ₅ acquired by the check node calculating unit 302 on the basis of information (matrix data) D305 representing the number of cyclic shifts of the unit matrix (or the quasi unit matrix) that is the origin in the transformed parity check matrix H′ performed in a corresponding branch and supplies a result thereof as messages D304 to the branch data storing memory 304.

The branch data storing memory 304 includes eighteen FIFOs 304 ₁ to 304 ₁₈, according to information D305 representing rows of the transformed parity check matrix H′ to which five messages D304 supplied from the cyclic shift circuit 303 of a previous stage belongs, selects a FIFO storing data from among the FIFOs 304 ₁ to 304 ₁₈, and sequentially stores the five messages D304 collectively in the selected FIFO. In order to read the data, the branch data storing memory 304 sequentially reads the five messages D306 ₁ from the FIFO 304 ₁ and supplies the read messages to the selector 305 of a next stage. After reading of the data from the FIFO 304 ₁ ends, the branch data storing memory 304 sequentially reads messages also from the FIFOs 304 ₂ to 304 ₁₈ and supplies the read messages to the selector 305.

The selector 305 selects the five messages supplied from the FIFO from which data is currently read from among the FIFOs 304 ₁ to 304 ₁₈ in accordance with a select signal D307 and supplies the selected messages as messages D308 to the variable node calculating unit 307 and the decoding word calculating unit 309.

Meanwhile, the reception data rearranging unit 310 rearranges the LDPC code D313, which corresponds to the parity check matrix H illustrated in FIG. 159, received through the communication line 13 by performing the column permutation represented in Equation (12) and supplies the rearranged LDPC code as reception data D314 to the reception data memory 306. The reception data memory 306 calculates a reception LLR (Log Likelihood Ratio) from the reception data D314 supplied from the reception data rearranging unit 310, stores the reception LLR, collects five reception LLRs, and supplies the reception LLRs as reception values D309 to the variable node calculating unit 307 and the decoding word calculating unit 309.

The variable node calculating unit 307 includes five variable node calculators 307 ₁ to 307 ₅, performs the variable node operation according to Equation (1) by using the messages D308 (D308 ₁ to D308 ₅) (messages u_(j) represented in Equation (1)) supplied through the selector 305 and the five reception values D309 (reception values u_(0i) represented in Equation (1)) supplied from the reception data memory 306, and supplies messages D310 (D310 ₁ to D310 ₅) (message v₁ represented in Equation (1)) acquired as an operation result to the cyclic shift circuit 308.

The cyclic shift circuit 308 cyclically shifts the messages D310 ₁ to D310 ₅ calculated by the variable node calculating unit 307 on the basis of information representing the number of cyclic shifts of the unit matrix (or the quasi unit matrix) that is the origin in the transformed parity check matrix H′ performed in a corresponding branch, and supplies a result thereof as messages D311 to the branch data storing memory 300.

By circulating the above operation in one cycle, decoding (the variable node operation and the check node operation) of the LDPC code can be performed once. After decoding the LDPC code a predetermined number of times, the decoding device illustrated in FIG. 162 acquires a final decoding result in the decoding word calculating unit 309 and the decoded data rearranging unit 311 and outputs the final decoding result.

In other words, the decoding word calculating unit 309 includes five decoding word calculators 309 ₁ to 309 ₅. The decoding word calculating unit 309 calculates a decoding result (decoding word) on the basis of Equation (5) as a final stage of a plurality of number of times of decoding by using the five messages D308 (D308 ₁ to D308 ₅) (messages u_(j) represented in Equation (5)) output by the selector 305 and the five reception values D309 (reception values u_(0i) represented in Equation (5)) supplied from the reception data memory 306 and supplies decoded data D315 acquired as a result thereof to the decoded data rearranging unit 311.

The decoded data rearranging unit 311 rearranges the order by performing reverse permutation of the column permutation represented in Equation (12) for the decoded data D315 supplied from the decoding word calculating unit 309 as a target and outputs the rearranged decoded data as a final decoding result D316.

As above, by performing one or both of row permutation and column permutation for the parity check matrix (original parity check matrix) and converting the parity check matrix into a parity check matrix (transformed parity check matrix) that can be represented by a combination of a P×P unit matrix, a quasi unit matrix acquired by setting one or more elements of “1” to “0”, a shifted matrix acquired by cyclically shifting the unit matrix or the quasi unit matrix, a sum matrix that is the sum of a plurality of unit matrixes, the quasi unit matrixes, and the shifted matrixes, and a P×P zero matrix, in other words, a parity check matrix (transformed parity check matrix) that can be represented by a combination of constitutive matrixes, as for LDPC code decoding, an architecture can be employed which simultaneously performs P check node operations and variable node operations, wherein P is smaller than the number of rows or the number of columns of the parity check matrix. In case of employing the architecture simultaneously performing P node operations (the (check node operations and the variable node operations) wherein P is a number less than the number of rows and the number of columns of the parity check matrix, compared to a case where the node operations corresponding to the same number as the number of rows and the number of columns of the parity check matrix are simultaneously performed, the operation frequency can be suppressed to be in a realizable range, and many repetitive decoding processes can be performed.

The LDPC decoder 166 that configures the receiving device 12 illustrated in FIG. 156, for example, performs the LDPC decoding by simultaneously performing P check node operations and variable node operations, similarly to the decoding device illustrated in FIG. 162.

In other words, for the simplification of description, in a case where the parity check matrix of the LDPC code output by the LDPC encoder 115 configuring the transmitting device 11 illustrated in FIG. 8 is the parity check matrix H illustrated in FIG. 159 in which the parity matrix has a staircase structure, in the parity interleaver 23 of the transmitting device 11, the parity interleave for interleaving the (K+qx+y+1)-th code bit into the position of the (K+Py+x+1)-th code bit is performed in a state in which the information length K is set to 60, the unit size P is set to 5, and the divisor q (=M/P) of the parity length M is set to 6.

Since the parity interleave, as described above, corresponds to the column permutation represented in Equation (12), the column permutation represented in Equation (12) does not need to be performed in the LDPC decoder 166.

For this reason, in the receiving device 12 illustrated in FIG. 156, as described above, the LDPC code for which the parity deinterleave has not been performed, in other words, the LDPC code in a state in which the column permutation represented in Equation (12) is performed is supplied from the group-wise deinterleaver 55 to the LDPC decoder 166. The LDPC decoder 166 performs a similar process as that of the decoding device illustrated in FIG. 162 except that the column permutation represented in Equation (12) is not performed.

In other words, FIG. 163 illustrates a configuration example of the LDPC decoder 166 illustrated in FIG. 156.

In FIG. 163, the LDPC decoder 166 has a similar configuration as the decoding device illustrated in FIG. 162 except that the reception data rearranging unit 310 illustrated in FIG. 162 is not arranged and performs a similar process as that of the decoding device illustrated in FIG. 162 except that the column permutation represented in Equation (12) is not performed, and thus, description thereof will not be presented.

As described above, since the LDPC decoder 166 can be configured without arranging the reception data rearranging unit 310, the scale thereof can be decreased to be less than that of the decoding device illustrated in FIG. 162.

Note that, in FIGS. 159 to 163, for the simplification of description, while the code length N of the LDPC code is set to 90, the information length K is set to 60, the unit size (the number of rows and the number of columns of the constitutive matrix) P is set to 5, and the divisor q (=M/P) of the parity length M is set to 6, the code length N, the information length K, the unit size P, and the divisor q (=M/P) are not limited to the values described above.

In other words, in the transmitting device 11 illustrated in FIG. 8, the LDPC encoder 115 outputs the LDPC code in which the code length N is set to 64800, 16200, or the like, the information length K is set to N−Pq (=N−M), the unit size P is set to 360, and the divisor q is set to M/P. However, the LDPC decoder 166 illustrated in FIG. 163 can be applied to a case where the LDPC decoding is performed by simultaneously performing P check node operations and variable node operations for the LDPC code as a target.

In addition, in a case where the parity portion of the decoding result is unnecessary, and only the information bits of the decoding result are output after the decoding of the LDPC code by the LDPC decoder 166, the LDPC decoder 166 may be configured without the decoded data rearranging unit 311.

<Configuration Example of Block Deinterleaver 54>

FIG. 164 is a block diagram that illustrates a configuration example of the block deinterleaver 54 illustrated in FIG. 157.

The block deinterleaver 54 has a configuration similar to the block interleaver 25 described above with reference to FIG. 94.

Thus, the block deinterleaver 54 includes the storage area called the part 1 and the storage area called the part 2, and each of the parts 1 and 2 is configured such that C columns as storage areas, which are equal in number to the number m of bits of the symbol, each storing one bit in the row direction and storing a predetermined number of bits in the column direction are arranged in the row direction.

The block deinterleaver 54 performs the block deinterleave by writing and reading the LDPC code for the parts 1 and 2.

However, in the block deinterleave, the writing of the LDPC code (forming the symbol) is performed in the order in which the LDPC code is read by the block interleaver 25 illustrated in FIG. 94.

In addition, in the block deinterleave, the reading of the LDPC code is performed in the order in which the LDPC code is written by the block interleaver 25 illustrated in FIG. 94.

In other words, in the block interleave performed by the block interleaver 25 illustrated in FIG. 94, while the LDPC code is written into the parts 1 and 2 in the column direction and is read from the parts 1 and 2 in the row direction, in the block deinterleave performed by the block deinterleaver 54 illustrated in FIG. 164, the LDPC code is written into the parts 1 and 2 in the row direction and is read from the parts 1 and 2 in the column direction.

<Another Configuration Example of Bit Deinterleaver 165>

FIG. 165 is a block diagram that illustrates another configuration example of the bit deinterleaver 165 illustrated in FIG. 156.

Note that, in the drawings, portions that correspond to the case illustrated in FIG. 157 are denoted using the same reference numerals, and, hereinafter, description thereof will not be presented as is appropriate.

In other words, the bit deinterleaver 165 illustrated in FIG. 165 has a similar configuration as that of the case illustrated in FIG. 157 except that a parity deinterleaver 1011 is newly arranged.

In the case illustrated in FIG. 165, the bit deinterleaver 165 is configured by a block deinterleaver 54, a group-wise deinterleaver 55, and a parity deinterleaver 1011 and performs bit deinterleave for the code bits of the LDPC code supplied from the demapper 164.

In other words, the block deinterleaver 54 performs block deinterleave (the inverse process of the block interleave) corresponding to the block interleave performed by the block interleaver 25 of the transmitting device 11, in other words, block deinterleave for restoring the positions of the code bits rearranged by the block interleave to the original positions for the LDPC code supplied from the demapper 164 as a target and supplies the LDPC code acquired as a result thereof to the group-wise deinterleaver 55.

The group-wise deinterleaver 55 performs group-wise deinterleave corresponding to the group-wise interleave as the rearrangement process performed by the group-wise interleaver 24 of the transmitting device 11 for the LDPC code supplied from the block deinterleaver 54 as a target.

The LDPC code that is acquired as a result of the group-wise deinterleave is supplied from the group-wise deinterleaver 55 to the parity deinterleaver 1011.

The parity deinterleaver 1011 performs the parity deinterleave (reverse processing of the parity interleave) corresponding to the parity interleave performed by the parity interleaver 23 of the transmitting device 11, in other words, the parity deinterleave for restoring the sequence of the code bits of the LDPC code of which the sequence has been changed by the parity interleave to the original sequence for the code bits after the group-wise deinterleave performed by the group-wise deinterleaver 55 as a target.

The LDPC code that is acquired as a result of the parity deinterleave is supplied from the parity deinterleaver 1011 to the LDPC decoder 166.

Therefore, in the bit deinterleaver 165 illustrated in FIG. 165, the LDPC code for which the block deinterleave, the group-wise deinterleave, and the parity deinterleave are performed, in other words, the LDPC code that is acquired by the LDPC coding according to the parity check matrix H is supplied to the LDPC decoder 166.

The LDPC decoder 166 performs LDPC decoding of the LDPC code supplied from the bit deinterleaver 165 by using the parity check matrix H used for the LDPC coding by the LDPC encoder 115 of the transmitting device 11. In other words, the LDPC decoder 166 performs the LDPC decoding of the LDPC code supplied from the bit deinterleaver 165 using the parity check matrix H (of the DVB type) used for the LDPC coding by the LDPC encoder 115 of the transmitting device 11 or the transformed parity check matrix acquired by performing at least the column permutation corresponding to the parity interleave for the parity check matrix H (for the ETRI type, the parity check matrix (FIG. 28) acquired by performing the column permutation for the parity check matrix (FIG. 27) used for the LDPC coding or the transformed parity check matrix (FIG. 29) acquired by performing the row permutation for the parity check matrix (FIG. 27) used for the LDPC coding).

In the case illustrated in FIG. 165, since the LDPC code that is acquired by the LDPC coding according to the parity check matrix H is supplied from the bit deinterleaver 165 (the parity deinterleaver 1011 thereof) to the LDPC decoder 166, in a case where the LDPC decoding of the LDPC code is performed using the parity check matrix H (of the DVB type) used by the LDPC encoder 115 of the transmitting device 11 for performing the LDPC coding (for the ETRI type, the parity check matrix (FIG. 28) acquired by performing the column permutation for the parity check matrix (FIG. 27) used for the LDPC coding), the LDPC decoder 166, for example, can be configured by a decoding device performing the LDPC decoding according to a full serial decoding scheme for sequentially performing operations of messages (a check node message and a variable node message) for each node or a decoding device performing the LDPC decoding according to a full parallel decoding scheme for simultaneously (in parallel) performing operations of messages for all the nodes.

In addition, in the LDPC decoder 166, in a case where the LDPC decoding of the LDPC code is performed using the transformed parity check matrix acquired by performing at least the column permutation corresponding to the parity interleave for the parity check matrix H (of the DVB type) used by the LDPC encoder 115 of the transmitting device 11 for performing the LDPC coding (for the ETRI type, the transformed parity check matrix (FIG. 29) acquired by performing the row permutation for the parity check matrix (FIG. 27) used for the LDPC coding), the LDPC decoder 166 can be configured by a decoding device that is a decoding device having an architecture simultaneously performing P (or a divisor of P other than 1) check node operations and variable node operations and the decoding device (FIG. 162) including the reception data rearranging unit 310 that rearranges the code bits of the LDPC code by performing a similar column permutation as the column permutation (parity interleave) for acquiring the transformed parity check matrix for the LDPC code.

Note that, in the case illustrated in FIG. 165, for the convenience of description, while the block deinterleaver 54 that performs the block deinterleave, the group-wise deinterleaver 55 that performs the group-wise deinterleave, and the parity deinterleaver 1011 that performs the parity deinterleave are separately configured, two or more of the block deinterleaver 54, the group-wise deinterleaver 55, and the parity deinterleaver 1011 may be configured integrally, similarly to the parity interleaver 23, the group-wise interleaver 24, and the block interleaver 25 of the transmitting device 11.

<Configuration Example of Reception System>

FIG. 166 is a block diagram illustrating a first configuration example of a reception system that can be applied to the receiving device 12.

In FIG. 166, the reception system includes an acquiring unit 1101, a transmission line decoding processing unit 1102, and an information source decoding processing unit 1103.

The acquiring unit 1101 acquires a signal including an LDPC code acquired by performing at least LDPC coding for LDPC target data such as video data or audio data of a program, for example, through a transmission line (communication line) not illustrated in the drawings such as terrestrial digital broadcasting, satellite digital broadcasting, a CATV network, the Internet, or other networks and supplies the acquired signal to the transmission line decoding processing unit 1102.

Here, in a case where the signal acquired by the acquiring unit 1101, for example, is broadcasted from a broadcasting station through a ground wave, a satellite wave, a Cable Television (CATV) network, or the like, the acquiring unit 1101 is configured by a tuner, a Set Top Box (STB), and the like. On the other hand, in a case where the signal acquired by the acquiring unit 1101, for example, is transmitted from a web server through multicasting like an Internet Protocol Television (IPTV), the acquiring unit 1101, for example, is configured by a network Interface (I/F) such as a Network Interface Card (NIC).

The transmission line decoding processing unit 1102 corresponds to the receiving device 12. The transmission line decoding processing unit 1102 performs transmission line decoding processing including at least processing for correcting an error generated in a transmission line for the signal acquired by the acquiring unit 1101 through the transmission line and supplies a signal acquired as a result thereof to the information source decoding processing unit 1103.

In other words, the signal that is acquired by the acquiring unit 1101 through the transmission line is a signal that is acquired by performing at least error correction coding for correcting an error generated in the transmission line. The transmission line decoding processing unit 1102 performs transmission line decoding processing such as error correction processing for such a signal.

Here, examples of the error correction coding include LDPC coding and BCH coding. Here, as the error correction coding, at least the LDPC coding is performed.

In addition, the transmission line decoding processing may include demodulation of a modulation signal or the like.

The information source decoding processing unit 1103 performs information source decoding processing including at least processing for extending compressed information to original information for the signal for which the transmission line decoding processing has been performed.

In other words, compression coding that compresses information may be performed for the signal acquired by the acquiring unit 1101 through the transmission line so as to decrease a data amount of a video or an audio as information. In such a case, the information source decoding processing unit 1103 performs the information source decoding processing such as the processing (extension processing) for extending the compressed information to the original information for the signal for which the transmission line decoding processing has been performed.

Note that, in a case where the compression coding has not been performed for the signal acquired by the acquiring unit 1101 through the transmission line, the processing for extending the compressed information to the original information is not performed by the information source decoding processing unit 1103.

In this case, as the extension processing, for example, there is MPEG decoding. In the transmission line decoding processing, in addition to the extension processing, descramble or the like may be included.

In the reception system configured as described above, in the acquiring unit 1101, for example, a signal for which the compression coding such as the MPEG coding and the error correction coding such as the LDPC coding have been performed for data such as a video or an audio is acquired through the transmission line and is supplied to the transmission line decoding processing unit 1102.

In the transmission line decoding processing unit 1102, for example, a similar processing as is performed by the receiving device 12 and the like are performed as the transmission line decoding processing for the signal supplied from the acquiring unit 1101, and a signal acquired as a result thereof is supplied to the information source decoding processing unit 1103.

In the information source decoding processing unit 1103, the information source decoding processing such as the MPEG decoding is performed for the signal supplied from the transmission line decoding processing unit 1102, and a video or an audio acquired as a result thereof is output.

The reception system illustrated in FIG. 166 as above can be applied to a television tuner that receives television broadcasting as digital broadcasting.

Note that each of the acquiring unit 1101, the transmission line decoding processing unit 1102, and the information source decoding processing unit 1103 can be configured as one independent device (hardware (Integrated Circuit (IC) or the like) or software module).

In addition, regarding the acquiring unit 1101, the transmission line decoding processing unit 1102, and the information source decoding processing unit 1103, a set of the acquiring unit 1101 and the transmission line decoding processing unit 1102, a set of the transmission line decoding processing unit 1102 and the information source decoding processing unit 1103, or a set of the acquiring unit 1101, the transmission line decoding processing unit 1102, and the information source decoding processing unit 1103 may be configured as one independent device.

FIG. 167 is a block diagram that illustrates a second configuration example of the reception system to which the receiving device 12 can be applied.

Note that, in the drawings, portions that correspond to those of the case illustrated in FIG. 166 are denoted using the same reference numerals, and hereinafter, description thereof will not be presented as is appropriate.

The reception system illustrated in FIG. 167 is common to the case illustrated in FIG. 166 in that the acquiring unit 1101, the transmission line decoding processing unit 1102, and the information source decoding processing unit 1103 are included but is different from the case illustrated in FIG. 166 in that an output unit 1111 is newly arranged.

The output unit 1111 is a display device displaying a video or a speaker outputting an audio and outputs a video or an audio as a signal output from the information source decoding processing unit 1103. In other words, the output unit 1111 displays the video or outputs the audio.

The reception system illustrated in FIG. 167 described above, for example, can be applied to a TV (television receiver) receiving television broadcasting as digital broadcasting, a radio receiver receiving radio broadcasting, or the like.

Note that, in a case where the compression coding is not performed for the signal acquired in the acquiring unit 1101, the signal that is output by the transmission line decoding processing unit 1102 is supplied to the output unit 1111.

FIG. 168 is a block diagram that illustrates a third configuration example of the reception system to which the receiving device 12 can be applied.

Note that, in the drawings, portions that correspond to those of the case illustrated in FIG. 166 are denoted using the same reference numerals, and, hereinafter, description thereof will not be presented as is appropriate.

The reception system illustrated in FIG. 168 is common to the case illustrated in FIG. 166 in that the acquiring unit 1101 and the transmission line decoding processing unit 1102 are arranged.

However, the reception system illustrated in FIG. 168 is different from the case illustrated in FIG. 166 in that the information source decoding processing unit 1103 is not arranged, but a recording unit 1121 is newly arranged.

The recording unit 1121 records (stores) a signal (for example, TS packets of TS of MPEG) output by the transmission line decoding processing unit 1102 on recording (storage) media such as an optical disk, a hard disk (magnetic disk), and a flash memory.

The reception system illustrated in FIG. 168 described above can be applied to a recorder that records television broadcasting and the like.

Note that, in FIG. 168, the reception system is configured by providing the information source decoding processing unit 1103 and can record the signal acquired by performing the information source decoding processing by the information source decoding processing unit 1103, in other words, the image or the sound acquired by decoding, by the recording unit 1121.

<Computer According to Embodiment>

A series of the processes described above can be performed either by hardware or by software. In a case where the series of the processes is performed by software, a program configuring the software is installed to a general-purpose computer or the like.

FIG. 169 is a diagram that illustrates an example of the configuration of a computer according to an embodiment to which the program executing the series of processes described above is installed.

The program may be recorded in a hard disk 705 or a ROM 703 as a recording medium built in the computer in advance.

Alternatively or additionally, the program may be stored (recorded) temporarily or perpetually on a removable recording medium 711 such as a flexible disk, a Compact Disc Read Only Memory (CD-ROM), a Magneto Optical (MO) disk, a Digital Versatile Disc (DVD), a magnetic disk, or a semiconductor memory. Such a removable recording medium 711 may be provided as so-called package software.

Note that, instead of installing the program to the computer from the removable recording medium 711 as described above, it may be configured such that the program is transmitted in a wireless manner from a download site to the computer through a digital broadcasting satellite or is transmitted to the computer in a wired manner through a network such as a local area network (LAN) or the Internet, and the computer receives the transmitted program using a communication unit 708 and installs the program to a built-in hard disk 705.

The computer has a central processing unit (CPU) 702 built therein, and an input/output interface 710 is connected to the CPU 702 through a bus 701. When an instruction is input from a user through the input/output interface 710 by operating an input unit 707 configured by a keyboard, a mouse, a microphone, and the like, the CPU 702 executes a program that is stored in a Read Only Memory (ROM) 703 in accordance with the instruction. Alternatively, the CPU 702 loads a program that is stored in the hard disk 705, a program that is transmitted from a satellite or a network, is received by the communication unit 708, and is installed to the hard disk 705, or a program that is read from the removable recording medium 711 loaded into a drive 709 and is installed to the hard disk 705 into a Random Access Memory (RAM) 704 and executes the program. Accordingly, the CPU 702 performs the process according to the flowchart described above or the process performed using the configuration illustrated in the block diagram described above. Then, the CPU 702, for example, outputs a result of the process from an output unit 706 configured by a Liquid Crystal Display (LCD), a speaker, and the like through the input/output interface 710, transmits the result from the communication unit 708, or records the result on the hard disk 705 as is necessary.

Here, in this specification, the processing step describing a program causing a computer to perform various processes does not need to be performed necessarily in a time series in accordance with the sequence described in the flowchart but also includes a process (for example, a parallel process or a process using an object) that is performed in a parallel manner or in an individual manner.

In addition, the program may be processed by one computer or may be processed by a plurality of computers in a distributed manner. Furthermore, the program may be transmitted to a remote computer and be executed.

Note that embodiments of the present technology are not limited to the embodiments described above, but various changes can be made therein in a range not departing from the concept of the present technology.

In other words, for example, the new LDPC code (the parity check matrix initial value table thereof) described above may be used when the communication line 13 (FIG. 7) is a satellite channel, a terrestrial wave, a cable (wired line) or any other communication channel. Furthermore, the new LDPC code can be used also for data transmission other than digital broadcasting.

In addition, the GW pattern described above can be applied to a code other than the new LDPC code. Furthermore, the modulation scheme to which the GW pattern described above is applied is not limited to the QPSK, the 16 QAM, the 64 QAM, the 256 QAM, and the 1024 QAM.

Note that the effects described in this specification are merely examples but are not for the purposes of limitation, and any additional effect may be present.

REFERENCE SIGNS LIST

-   11 Transmitting device -   12 Receiving device -   23 Parity interleaver -   24 Group-wise interleaver -   Block interleaver -   54 Block deinterleaver -   55 Group-wise deinterleaver -   111 Mode adaptation/multiplexer -   112 Padder -   113 BB scrambler -   114 BCH encoder -   115 LDPC encoder -   116 Bit interleaver -   117 Mapper -   118 Time interleaver -   119 SISO/MISO encoder -   120 Frequency interleaver -   121 BCH encoder -   122 LDPC encoder -   123 Mapper -   124 Frequency interleaver -   131 Frame builder/resource allocation unit -   132 OFDM generating unit -   151 OFDM processing unit -   152 Frame managing unit -   153 Frequency deinterleaver -   154 Demapper -   155 LDPC decoder -   156 BCH decoder -   161 Frequency deinterleaver -   162 SISO/MISO decoder -   163 Time deinterleaver -   164 Demapper -   165 Bit deinterleaver -   166 LDPC decoder -   167 BCH decoder -   168 BB descrambler -   169 Null deletion unit -   170 Demultiplexer -   300 Branch data storing memory -   301 Selector -   302 Check node calculating unit -   303 Cyclic shift circuit -   304 Branch data storing memory -   305 Selector -   306 Reception data memory -   307 Variable node calculating unit -   308 Cyclic shift circuit -   309 Decoding word calculating unit -   310 Reception data rearranging unit -   311 Decoded data rearranging unit -   601 Coding processing unit -   602 Storage unit -   611 Coding rate setting unit -   612 Initial value table reading unit -   613 Parity check matrix generating unit -   614 Information bit reading unit -   615 Coding parity calculating unit -   616 Control unit -   701 Bus -   702 CPU -   703 ROM -   704 RAM -   705 Hard disk -   706 Output unit -   707 Input unit -   708 Communication unit -   709 Drive -   710 Input/output interface -   711 Removable recording medium -   1001 Reverse permutation unit -   1002 Memory -   1011 Parity deinterleaver -   1101 Acquiring unit -   1101 Transmission line decoding processing unit -   1103 Information source decoding processing unit -   1111 Output unit -   1121 Recording unit 

The invention claimed is:
 1. A receiving device for receiving digital television signals, the receiving device comprising: a receiver configured to receive encoded data, each ten bits of which mapped to one of 1024 signal points of a modulation method; and processing circuitry configured to process the encoded data to produce a group-wise interleaved low density parity check (LDPC) codeword; process the group-wise interleaved LDPC codeword in a unit of a bit group of 360 bits to produce an LDPC codeword of an LDPC code; wherein an (i+1)-th bit group from a head of the LDPC codeword of the LDPC code is indicated by a bit group i, the LDPC codeword of the LDPC codeword has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC codeword has a following sequence of bit groups, 49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175, decode the LDPC codeword of the LDPC code to produce decoded data; and process the decoded data for presentation; wherein the LDPC code has a length N of 64800 bits and a coding rate r of 13/15 and corresponds to a parity check matrix initial value table including the following, 142 2307 2598 2650 4028 4434 5781 5881 6016 6323 6681 6698 8125 2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 8539 8583 899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602 21 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616 20 1745 2838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631 9 6274 6725 6792 7195 7333 8027 8186 8209 8273 8442 8548 8632 494 1365 2405 3799 5188 5291 7644 7926 8139 8458 8504 8594 8625 192 574 1179 4387 4695 5089 5831 7673 7789 8298 8301 8612 8632 11 20 1406 6111 6176 6256 6708 6834 7828 8232 8457 8495 8602 6 2654 3554 4483 4966 5866 6795 8069 8249 8301 8497 8509 8623 21 1144 2355 3124 6773 6805 6887 7742 7994 8358 8374 8580 8611 335 4473 4883 5528 6096 7543 7586 7921 8197 8319 8394 8489 8636 2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 8544 8586 8617 12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 8137 710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619 200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526 3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636 3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598 105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587 787 1857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537 15 1118 4226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568 36 5216 5368 5616 6029 6591 8038 8067 8299 8351 8565 8578 8585 1 23 4300 4530 5426 5532 5817 6967 7124 7979 8022 8270 8437 629 2133 4828 5475 5875 5890 7194 8042 8345 8385 8518 8598 8612 11 1065 3782 4237 4993 7104 7863 7904 8104 8228 8321 8383 8565 2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 8527 8557 8614 5600 6591 7491 7696 1766 8281 8626 1725 2280 5120 1650 3445 7652 4312 6911 8626 15 1013 5892 2263 2546 2979 1545 5873 7406 67 726 3697 2860 6443 8542 17 911 2820 1561 4580 6052 79 5269 7134 22 2410 2424 3501 5642 8627 808 6950 8571 4099 6389 7482 4023 5000 7833 5476 5765 7917 1008 3194 7207 20 495 5411 1703 8388 8635 6 4395 4921 200 2053 8206 1089 5126 5562 10 4193 7720 1967 2151 4608 22 738 3513 3385 5066 8152 440 1118 8537 3429 6058 7716 5213 7519 8382 5564 8365 8620 43 3219 8603 4 5409 5815 5 6376 7654 4091 5724 5953 5348 6754 8613 1634 6398 6632 72 2058 8605 3497 5811 7579 3846 6743 8559 15 5933 8629 2133 5859 7068 4151 4617 8566 2960 8270 8410 2059 3617 8210 544 1441 6895 4043 7482 8592 294 2180 8524 3058 8227 8373 364 5756 8617 5383 8555 8619 1704 2480 4181 7338 7929 7990 2615 3905 7981 4298 4548 8296 8262 8319 8630 892 1893 8028 5694 7237 8595 1487 5012 5810 4335 8593 8624 3509 4531 5273 10 22 830 4161 5208 6280 275 7063 8634 4 2725 3113 2279 7403 8174 1637 3328 3930 2810 4939 5624 3 1234 7687 2799 7740 8616 22 7701 8636 4302 7857 7993 7477 7794 8592 9 6111 8591 5 8606 8628 347 3497 4033 1747 2613 8636 1827 5600 7042 580 1822 6842 232 7134 7783 4629 5000 7231 951 2806 4947 571 3474 8577 2437 2496 7945 23 5873 8162 12 1168 7686 8315 8540 8596 1766 2506 4733 929 1516 3338 21 1216 6555 782 1452 8617 8 6083 6087 667 3240 4583 4030 4661 5790 559 7122 8553 3202 4388 4909 2533 3673 8594 1991 3954 6206 6835 7900 7980 189 5722 8573 2680 4928 4998 243 2579 7735 4281 8132 8566 7656 7671 8609 1116 2291 4166 21 388 8021 6 1123 8369 311 4918 8511 0 3248 6290 13 6762 7172 4209 5632 7563 49 127 8074 581 1735 4075 0 2235 5470 2178 5820 6179 16 3575 6054 1095 4564 6458 9 1581 5953 2537 6469 8552 14 3874 4844 0 3269 3551 2114 7372 7926 1875 2388 4057 3232 4042 6663 9 401 583 13 4100 6584 2299 4190 4410 21 3670
 4979. 2. The receiving device according to claim 1, wherein the LDPC code uses a parity check matrix, which includes an information matrix part and a parity matrix part.
 3. The receiving device according to claim 2, wherein the LDPC codeword includes information bits and parity bits; and the information matrix part corresponds to the information bits and the parity matrix part corresponds to the parity bits.
 4. The receiving device according to claim 3, wherein the parity matrix part is a lower bidiagonal matrix, in which elements of “1” are arranged in a step-wise fashion.
 5. The receiving device according to claim 3, wherein the information matrix part is represented by the parity check matrix initial value table, and the parity check matrix initial value table is a table showing in an i-th row, i>0, positions of elements “1” in (1+360×(i−1))-th column of the information matrix part.
 6. The receiving device according to claim 5, wherein if a length of the parity bit of the LDPC codeword is represented by M, the z+360×(i−1)-th column of the parity check matrix, z>1, is obtained by the cyclic shift of the (z−1)+360×(i−1)-th column of the parity check matrix indicating a position of an element “1” in the parity check matrix initial value table downward by q=M/360.
 7. The receiving device according to claim 6, wherein as for each column from the 2+360×(i−1)-th column to a 360×i-th column being the column other than the 1+360×(i−1)-th column of the parity check matrix, if an i-th row j-th column value of the parity check matrix initial value table is represented as hi, j and the row number of a j-th element “1” of a w-th column of the parity check matrix is represented as Hw-j, a row number Hw-j of the j-th element “1” of the w-th column being the column other than the 1+360×(i−1)-th column of the parity check matrix is represented by the equation Hw-j=mod(hi,j+mod((w−1),360)×M/360,M).
 8. The receiving device according to claim 2, wherein the parity check matrix has no cycle-4.
 9. The receiving device according to claim 1, wherein the input is a tuner.
 10. The receiving device according to claim 1, wherein the modulation scheme employs non-uniform constellations (NUCs).
 11. A method performed by a receiving device receiving digital television signals, the method comprising: receiving encoded data, each 10 bits of which mapped to one of 1024 signal points of a modulation method; processing the encoded data to produce a group-wise interleaved low density parity check (LDPC) codeword; processing the group-wise interleaved LDPC codeword in a unit of a bit group of 360 bits to produce an LDPC codeword of an LDPC code; wherein an (i+1)-th bit group from a head of the LDPC codeword of the LDPC code is indicated by a bit group i, the LDPC codeword of the LDPC code has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC codeword has a following sequence of bit groups, 49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175, decoding the LDPC codeword of the LDPC code to produce decoded data; and processing the decoded data for presentation; wherein the LDPC code has a length N of 64800 bits and a coding rate r of 13/15 and corresponds to a parity check matrix initial value table including the following, 142 2307 2598 2650 4028 4434 5781 5881 6016 6323 6681 6698 8125 2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 8539 8583 899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602 21 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616 20 1745 2838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631 9 6274 6725 6792 7195 7333 8027 8186 8209 8273 8442 8548 8632 494 1365 2405 3799 5188 5291 7644 7926 8139 8458 8504 8594 8625 192 574 1179 4387 4695 5089 5831 7673 7789 8298 8301 8612 8632 11 20 1406 6111 6176 6256 6708 6834 7828 8232 8457 8495 8602 6 2654 3554 4483 4966 5866 6795 8069 8249 8301 8497 8509 8623 21 1144 2355 3124 6773 6805 6887 7742 7994 8358 8374 8580 8611 335 4473 4883 5528 6096 7543 7586 7921 8197 8319 8394 8489 8636 2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 8544 8586 8617 12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 8137 710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619 200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526 3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636 3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598 105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587 787 1857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537 15 1118 4226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568 36 5216 5368 5616 6029 6591 8038 8067 8299 8351 8565 8578 8585 1 23 4300 4530 5426 5532 5817 6967 7124 7979 8022 8270 8437 629 2133 4828 5475 5875 5890 7194 8042 8345 8385 8518 8598 8612 11 1065 3782 4237 4993 7104 7863 7904 8104 8228 8321 8383 8565 2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 8527 8557 8614 5600 6591 7491 7696 1766 8281 8626 1725 2280 5120 1650 3445 7652 4312 6911 8626 15 1013 5892 2263 2546 2979 1545 5873 7406 67 726 3697 2860 6443 8542 17 911 2820 1561 4580 6052 79 5269 7134 22 2410 2424 3501 5642 8627 808 6950 8571 4099 6389 7482 4023 5000 7833 5476 5765 7917 1008 3194 7207 20 495 5411 1703 8388 8635 6 4395 4921 200 2053 8206 1089 5126 5562 10 4193 7720 1967 2151 4608 22 738 3513 3385 5066 8152 440 1118 8537 3429 6058 7716 5213 7519 8382 5564 8365 8620 43 3219 8603 4 5409 5815 5 6376 7654 4091 5724 5953 5348 6754 8613 1634 6398 6632 72 2058 8605 3497 5811 7579 3846 6743 8559 15 5933 8629 2133 5859 7068 4151 4617 8566 2960 8270 8410 2059 3617 8210 544 1441 6895 4043 7482 8592 294 2180 8524 3058 8227 8373 364 5756 8617 5383 8555 8619 1704 2480 4181 7338 7929 7990 2615 3905 7981 4298 4548 8296 8262 8319 8630 892 1893 8028 5694 7237 8595 1487 5012 5810 4335 8593 8624 3509 4531 5273 10 22 830 4161 5208 6280 275 7063 8634 4 2725 3113 2279 7403 8174 1637 3328 3930 2810 4939 5624 3 1234 7687 2799 7740 8616 22 7701 8636 4302 7857 7993 7477 7794 8592 9 6111 8591 5 8606 8628 347 3497 4033 1747 2613 8636 1827 5600 7042 580 1822 6842 232 7134 7783 4629 5000 7231 951 2806 4947 571 3474 8577 2437 2496 7945 23 5873 8162 12 1168 7686 8315 8540 8596 1766 2506 4733 929 1516 3338 21 1216 6555 782 1452 8617 8 6083 6087 667 3240 4583 4030 4661 5790 559 7122 8553 3202 4388 4909 2533 3673 8594 1991 3954 6206 6835 7900 7980 189 5722 8573 2680 4928 4998 243 2579 7735 4281 8132 8566 7656 7671 8609 1116 2291 4166 21 388 8021 6 1123 8369 311 4918 8511 0 3248 6290 13 6762 7172 4209 5632 7563 49 127 8074 581 1735 4075 0 2235 5470 2178 5820 6179 16 3575 6054 1095 4564 6458 9 1581 5953 2537 6469 8552 14 3874 4844 0 3269 3551 2114 7372 7926 1875 2388 4057 3232 4042 6663 9 401 583 13 4100 6584 2299 4190 4410 21 3670
 4979. 12. The method according to claim 11, wherein the LDPC code uses a parity check matrix, which includes an information matrix part and a parity matrix part.
 13. The method according to claim 12, wherein the LDPC codeword includes information bits and parity bits; and the information matrix part corresponds to the information bits and the parity matrix part corresponds to the parity bits.
 14. The method according to claim 13, wherein the parity matrix part is a lower bidiagonal matrix, in which elements of “1” are arranged in a step-wise fashion.
 15. The method according to claim 13, wherein the information matrix part is represented by the parity check matrix initial value table, and the parity check matrix initial value table is a table showing in an i-th row, i>0, positions of elements “1” in (1+360×(i−1))-th column of the information matrix part.
 16. The method according to claim 15, wherein if a length of the parity bit of the LDPC codeword is represented by M, the z+360×(i−1)-th column of the parity check matrix, z>1, is obtained by the cyclic shift of the (z−1)+360×(i−1)-th column of the parity check matrix indicating a position of an element “1” in the parity check matrix initial value table downward by q=M/360.
 17. The method according to claim 16, wherein as for each column from the 2+360×(i−1)-th column to a 360×i-th column being the column other than the 1+360×(i−1)-th column of the parity check matrix, if an i-th row j-th column value of the parity check matrix initial value table is represented as hi, j and the row number of a j-th element “1” of a w-th column of the parity check matrix is represented as Hw-j, a row number Hw-j of the j-th element “1” of the w-th column being the column other than the 1+360×(i−1)-th column of the parity check matrix is represented by the equation Hw-j=mod(hi,j+mod((w−1),360)×M/360,M).
 18. The method according to claim 12, wherein the parity check matrix has no cycle-4.
 19. The method according to claim 11, wherein receiving the encoded data further comprises receiving the encoded data by means of a tuner.
 20. A non-transitory computer readable medium including computer executable instructions which, when executed by a computer, cause the computer to perform a method comprising: receiving encoded data, each 10 bits of which mapped to one of 1024 signal points of a modulation method; processing the encoded data to produce a group-wise interleaved low density parity check (LDPC) codeword; processing the group-wise interleaved LDPC codeword in a unit of a bit group of 360 bits to produce an LDPC codeword of an LDPC code; wherein an (i+1)-th bit group from a head of the LDPC codeword of the LDPC code is indicated by a bit group i, the LDPC codeword of the LDPC code has a sequence of bit groups 0 to 179, and the group-wise interleaved LDPC codeword has a following sequence of bit groups, 49, 2, 57, 47, 31, 35, 24, 39, 59, 0, 45, 41, 55, 53, 51, 37, 33, 43, 56, 38, 48, 32, 50, 23, 34, 54, 1, 36, 44, 52, 40, 58, 122, 46, 42, 30, 3, 75, 73, 65, 145, 71, 79, 67, 69, 83, 85, 147, 63, 81, 77, 61, 5, 26, 62, 64, 74, 70, 82, 149, 76, 4, 78, 84, 80, 86, 66, 68, 72, 6, 60, 154, 103, 95, 101, 143, 9, 89, 141, 128, 97, 137, 133, 7, 13, 99, 91, 93, 87, 11, 136, 90, 88, 94, 10, 8, 14, 96, 104, 92, 132, 142, 100, 98, 12, 102, 152, 139, 150, 106, 146, 130, 27, 108, 153, 112, 114, 29, 110, 134, 116, 15, 127, 125, 123, 120, 148, 151, 113, 126, 124, 135, 129, 109, 25, 28, 158, 117, 105, 115, 111, 131, 107, 121, 18, 170, 164, 20, 140, 160, 166, 162, 119, 155, 168, 178, 22, 174, 172, 176, 16, 157, 159, 171, 161, 118, 17, 163, 21, 165, 19, 179, 177, 167, 138, 173, 156, 144, 169, and 175, decoding the LDPC codeword of the LDPC code to produce decoded data; and processing the decoded data for presentation; wherein the LDPC code has a length N of 64800 bits and a coding rate r of 13/15 and corresponds to a parity check matrix initial value table including the following, 142 2307 2598 2650 4028 4434 5781 5881 6016 6323 6681 6698 8125 2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 8539 8583 899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602 21 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616 20 1745 2838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631 9 6274 6725 6792 7195 7333 8027 8186 8209 8273 8442 8548 8632 494 1365 2405 3799 5188 5291 7644 7926 8139 8458 8504 8594 8625 192 574 1179 4387 4695 5089 5831 7673 7789 8298 8301 8612 8632 11 20 1406 6111 6176 6256 6708 6834 7828 8232 8457 8495 8602 6 2654 3554 4483 4966 5866 6795 8069 8249 8301 8497 8509 8623 21 1144 2355 3124 6773 6805 6887 7742 7994 8358 8374 8580 8611 335 4473 4883 5528 6096 7543 7586 7921 8197 8319 8394 8489 8636 2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 8544 8586 8617 12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 8137 710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619 200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526 3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636 3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598 105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587 787 1857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537 15 1118 4226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568 36 5216 5368 5616 6029 6591 8038 8067 8299 8351 8565 8578 8585 1 23 4300 4530 5426 5532 5817 6967 7124 7979 8022 8270 8437 629 2133 4828 5475 5875 5890 7194 8042 8345 8385 8518 8598 8612 11 1065 3782 4237 4993 7104 7863 7904 8104 8228 8321 8383 8565 2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 8527 8557 8614 5600 6591 7491 7696 1766 8281 8626 1725 2280 5120 1650 3445 7652 4312 6911 8626 15 1013 5892 2263 2546 2979 1545 5873 7406 67 726 3697 2860 6443 8542 17 911 2820 1561 4580 6052 79 5269 7134 22 2410 2424 3501 5642 8627 808 6950 8571 4099 6389 7482 4023 5000 7833 5476 5765 7917 1008 3194 7207 20 495 5411 1703 8388 8635 6 4395 4921 200 2053 8206 1089 5126 5562 10 4193 7720 1967 2151 4608 22 738 3513 3385 5066 8152 440 1118 8537 3429 6058 7716 5213 7519 8382 5564 8365 8620 43 3219 8603 4 5409 5815 5 6376 7654 4091 5724 5953 5348 6754 8613 1634 6398 6632 72 2058 8605 3497 5811 7579 3846 6743 8559 15 5933 8629 2133 5859 7068 4151 4617 8566 2960 8270 8410 2059 3617 8210 544 1441 6895 4043 7482 8592 294 2180 8524 3058 8227 8373 364 5756 8617 5383 8555 8619 1704 2480 4181 7338 7929 7990 2615 3905 7981 4298 4548 8296 8262 8319 8630 892 1893 8028 5694 7237 8595 1487 5012 5810 4335 8593 8624 3509 4531 5273 10 22 830 4161 5208 6280 275 7063 8634 4 2725 3113 2279 7403 8174 1637 3328 3930 2810 4939 5624 3 1234 7687 2799 7740 8616 22 7701 8636 4302 7857 7993 7477 7794 8592 9 6111 8591 5 8606 8628 347 3497 4033 1747 2613 8636 1827 5600 7042 580 1822 6842 232 7134 7783 4629 5000 7231 951 2806 4947 571 3474 8577 2437 2496 7945 23 5873 8162 12 1168 7686 8315 8540 8596 1766 2506 4733 929 1516 3338 21 1216 6555 782 1452 8617 8 6083 6087 667 3240 4583 4030 4661 5790 559 7122 8553 3202 4388 4909 2533 3673 8594 1991 3954 6206 6835 7900 7980 189 5722 8573 2680 4928 4998 243 2579 7735 4281 8132 8566 7656 7671 8609 1116 2291 4166 21 388 8021 6 1123 8369 311 4918 8511 0 3248 6290 13 6762 7172 4209 5632 7563 49 127 8074 581 1735 4075 0 2235 5470 2178 5820 6179 16 3575 6054 1095 4564 6458 9 1581 5953 2537 6469 8552 14 3874 4844 0 3269 3551 2114 7372 7926 1875 2388 4057 3232 4042 6663 9 401 583 13 4100 6584 2299 4190 4410 21 367
 04979. 